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Fig. 8: The relative abundance of light elements to Hidrogen. Note the large range of scales involved. From Ref. [17]

Figure 8 The relative abundance of light elements to Hidrogen. Note the large range of scales involved. From Ref. [17]

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Fig. 1: Parameter space (Qaz, 2a). The green (dashed) line Q, = 1 — OQ, corresponds to a flat universe, Qx% = 0, separating open from closed universes. The blue (dotted) line Qa = Qa,/2 corresponds to uniform expansion, qo = 0, separating accelerating from decelerating universes. The violet (dot-dashed) line corresponds to critical universes, separating eternal expansion from recollapse in the future. Finally, the red (continuous) lines correspond to toHo = 0.5, 0.6,..., co, beyond which the universe has a bounce.
Fig. 1: Parameter space (Qaz, 2a). The green (dashed) line Q, = 1 — OQ, corresponds to a flat universe, Qx% = 0, separating open from closed universes. The blue (dotted) line Qa = Qa,/2 corresponds to uniform expansion, qo = 0, separating accelerating from decelerating universes. The violet (dot-dashed) line corresponds to critical universes, separating eternal expansion from recollapse in the future. Finally, the red (continuous) lines correspond to toHo = 0.5, 0.6,..., co, beyond which the universe has a bounce.
Fig. 2: The Type Ia supernovae observed nearby show a relationship between their absolute luminosity and the timescale of their light curve: the brighter supemovae are slower and the fainter ones are faster. A simple linear relation between the absolute magnitude and a “stretch factor” multiplying the light curve timescale fits the data quite well. From Ref. [7]. which is just a kinematical effect (we have not included yet any dynamics, i.e. the matter content the universe). Note that at low redshift (z < 1), one is tempted to associate the observed change i wavelength with a Doppler effect due to a hypothetical recession velocity of the distant galaxy. Th is only an approximation. In fact, the redshift cannot be ascribed to the relative velocity of the distar galaxy because in general relativity (i.e. in curved spacetimes) one cannot compare velocities throug parallel transport, since the value depends on the path! If the distance to the galaxy is small, i.e. 2 <_ the physical spacetime is not very different from Minkowsky and such a comparison is approximatel valid. As z becomes of order one, such a relation is manifestly false: galaxies cannot travel at speec greater than the speed of light; it is the stretching of spacetime which is responsible for the observe redshift.
Fig. 2: The Type Ia supernovae observed nearby show a relationship between their absolute luminosity and the timescale of their light curve: the brighter supemovae are slower and the fainter ones are faster. A simple linear relation between the absolute magnitude and a “stretch factor” multiplying the light curve timescale fits the data quite well. From Ref. [7]. which is just a kinematical effect (we have not included yet any dynamics, i.e. the matter content the universe). Note that at low redshift (z < 1), one is tempted to associate the observed change i wavelength with a Doppler effect due to a hypothetical recession velocity of the distant galaxy. Th is only an approximation. In fact, the redshift cannot be ascribed to the relative velocity of the distar galaxy because in general relativity (i.e. in curved spacetimes) one cannot compare velocities throug parallel transport, since the value depends on the path! If the distance to the galaxy is small, i.e. 2 <_ the physical spacetime is not very different from Minkowsky and such a comparison is approximatel valid. As z becomes of order one, such a relation is manifestly false: galaxies cannot travel at speec greater than the speed of light; it is the stretching of spacetime which is responsible for the observe redshift.
Fig. 3: Upper panel: The Hubble diagram in linear redshift scale. Supernovae with Az < 0.01 of eachother have been weighted-averaged binned. The solid curve represents the best-fit flat universe model, (Qaz = 0.25, Qa = 0.75). Two other cosmological models are shown for comparison, (Qaz = 0.25, Qa = 0) and (Qn7 = 1, Qa = 0). Lower panel: Residuals of the averaged data relative to an empty universe. From Ref. [7]. Nowadays, we are beginning to probe much greater distances, corresponding to z ~ 1, thanks to type Ia supernovae. These are white dwarf stars at the end of their life cycle that accrete matter from a companion until they become unstable and violently explode in a natural thermonuclear explosion that out-shines their progenitor galaxy. The intensity of the distant flash varies in time, it takes about three weeks to reach its maximum brightness and then it declines over a period of months. Although the maximum luminosity varies from one supernova to another, depending on their original mass, their environment, etc., there is a pattern: brighter explosions last longer than fainter ones. By studying the characteristic light curves, see Fig. 2, of a reasonably large statistical sample, cosmologists from the Supemova Cosmology Project [7] and the High-redshift Supernova Project [9], are now quite confident that they can use this type of supernova as a standard candle. Since the light coming from some of these rare explosions has travelled a large fraction of the size of the universe, one expects to be able to infer from their distribution the spatial curvature and the rate of expansion of the universe.
Fig. 3: Upper panel: The Hubble diagram in linear redshift scale. Supernovae with Az < 0.01 of eachother have been weighted-averaged binned. The solid curve represents the best-fit flat universe model, (Qaz = 0.25, Qa = 0.75). Two other cosmological models are shown for comparison, (Qaz = 0.25, Qa = 0) and (Qn7 = 1, Qa = 0). Lower panel: Residuals of the averaged data relative to an empty universe. From Ref. [7]. Nowadays, we are beginning to probe much greater distances, corresponding to z ~ 1, thanks to type Ia supernovae. These are white dwarf stars at the end of their life cycle that accrete matter from a companion until they become unstable and violently explode in a natural thermonuclear explosion that out-shines their progenitor galaxy. The intensity of the distant flash varies in time, it takes about three weeks to reach its maximum brightness and then it declines over a period of months. Although the maximum luminosity varies from one supernova to another, depending on their original mass, their environment, etc., there is a pattern: brighter explosions last longer than fainter ones. By studying the characteristic light curves, see Fig. 2, of a reasonably large statistical sample, cosmologists from the Supemova Cosmology Project [7] and the High-redshift Supernova Project [9], are now quite confident that they can use this type of supernova as a standard candle. Since the light coming from some of these rare explosions has travelled a large fraction of the size of the universe, one expects to be able to infer from their distribution the spatial curvature and the rate of expansion of the universe.
Fig. 4: The Supernovae Ia residual Hubble diagram. Upper panel: Ground-based discoveries are represented by diamonds, HST-discovered SNe Ia are shown as filled circles. Lower panel: The same but with weighted averaged in fixed redshift bins. Kinematic models of the expansion history are shown relative to an eternally coasting model g(z) = 0. From Ref. [[2).
Fig. 4: The Supernovae Ia residual Hubble diagram. Upper panel: Ground-based discoveries are represented by diamonds, HST-discovered SNe Ia are shown as filled circles. Lower panel: The same but with weighted averaged in fixed redshift bins. Kinematic models of the expansion history are shown relative to an eternally coasting model g(z) = 0. From Ref. [[2).
Fig. 5: The recent supernovae data on the (Qar, Qa) plane. Shown are the 1-, 2- and 3-o contours, as well as the data from 1998, for comparison. It is clear that the old EdS cosmological model at (Qar = 1, Qa = 0) is many standard deviations away from the data. From Ref. [12]. When substituting Q, ~ 0.7 and Qy, ~ 0.3, one obtains z, ~ 0.6, in excellent agreement with recent observations [12]. The plane (Q,, 2,) can be seen in Fig. 5, which shows a significant improvement with respect to previous data.
Fig. 5: The recent supernovae data on the (Qar, Qa) plane. Shown are the 1-, 2- and 3-o contours, as well as the data from 1998, for comparison. It is clear that the old EdS cosmological model at (Qar = 1, Qa = 0) is many standard deviations away from the data. From Ref. [12]. When substituting Q, ~ 0.7 and Qy, ~ 0.3, one obtains z, ~ 0.6, in excellent agreement with recent observations [12]. The plane (Q,, 2,) can be seen in Fig. 5, which shows a significant improvement with respect to previous data.
Fig. 6: Ordinary matter dilutes as it expands. According to the second law of Thermodynamics, its pressure on the walls should be positive, which excerts a force, and energy is lost in the expansion. On the other hand, vacuum energy is always the same, independent of the volume of the region, and thus, according to the second law, its pressure must be negative and of the same magnitude as the energy density. This negative pressure means that the volume tends to increase more and more rapidly, which explains the exponential expansion of the universe dominated by a cosmological constant. Even if we assumed that the ultraviolet cutoff associated with quantum gravity was as low as the elec- troweak scale (and thus around the corner, liable to be explored in the LHC), the theoretical expectation would still be 60 orders of magnitude too big. This is by far the worst mismatch between theory and observations in all of science. There must be something seriously wrong in our present understanding of gravity at the most fundamental level. Perhaps we don’t understand the vacuum and its energy does not gravitate after all, or perhaps we need to impose a new principle (or a symmetry) at the quantum gravity level to accommodate such a flagrant mismatch. Fig. 6: Ordinary matter dilutes as it expands. According to the second law of Thermodynamics, its pressure on the walls should
Fig. 6: Ordinary matter dilutes as it expands. According to the second law of Thermodynamics, its pressure on the walls should be positive, which excerts a force, and energy is lost in the expansion. On the other hand, vacuum energy is always the same, independent of the volume of the region, and thus, according to the second law, its pressure must be negative and of the same magnitude as the energy density. This negative pressure means that the volume tends to increase more and more rapidly, which explains the exponential expansion of the universe dominated by a cosmological constant. Even if we assumed that the ultraviolet cutoff associated with quantum gravity was as low as the elec- troweak scale (and thus around the corner, liable to be explored in the LHC), the theoretical expectation would still be 60 orders of magnitude too big. This is by far the worst mismatch between theory and observations in all of science. There must be something seriously wrong in our present understanding of gravity at the most fundamental level. Perhaps we don’t understand the vacuum and its energy does not gravitate after all, or perhaps we need to impose a new principle (or a symmetry) at the quantum gravity level to accommodate such a flagrant mismatch. Fig. 6: Ordinary matter dilutes as it expands. According to the second law of Thermodynamics, its pressure on the walls should
Table 1: The internal degrees of freedom of various fundamental particles. In order to understand the thermodynamical behaviour of a plasma of different species of particles at high temperatures we will consider a gas of particles with g internal degrees of freedom weakly interacting. The degrees of freedom corresponding to the different particles can be seen in Table 1. For example, leptons and quarks have 4 degrees of freedom since they correspond to the two helicities for both particle and antiparticle. However, the nature of neutrinos is still unknown. If they happen to be Majorana fermions, then they would be their own antiparticle and the number of degrees of freedom would reduce to 2. For photons and gravitons (without mass) their 2 d.o.f. correspond to their states of polarization. The 8 gluons (also without mass) are the gauge bosons responsible for the strong interaction betwen quarks, and also have 2 d.o.f. each. The vector bosons W~ and Z° are massive and thus, apart from the transverse components of the polarization, they also have longitudinal components. For each of these particles we can compute the number density n, the energy density p and the pressure p, in thermal equilibrium at a given temperature T,
Table 1: The internal degrees of freedom of various fundamental particles. In order to understand the thermodynamical behaviour of a plasma of different species of particles at high temperatures we will consider a gas of particles with g internal degrees of freedom weakly interacting. The degrees of freedom corresponding to the different particles can be seen in Table 1. For example, leptons and quarks have 4 degrees of freedom since they correspond to the two helicities for both particle and antiparticle. However, the nature of neutrinos is still unknown. If they happen to be Majorana fermions, then they would be their own antiparticle and the number of degrees of freedom would reduce to 2. For photons and gravitons (without mass) their 2 d.o.f. correspond to their states of polarization. The 8 gluons (also without mass) are the gauge bosons responsible for the strong interaction betwen quarks, and also have 2 d.o.f. each. The vector bosons W~ and Z° are massive and thus, apart from the transverse components of the polarization, they also have longitudinal components. For each of these particles we can compute the number density n, the energy density p and the pressure p, in thermal equilibrium at a given temperature T,
On the other hand, fora non-relativistic gas (m >> T), with arbitrary chemical potential j., we find
On the other hand, fora non-relativistic gas (m >> T), with arbitrary chemical potential j., we find
Fig. 7: the light degrees of freedom g, and g.5 as a function of the temperature of the universe. From Ref. [[[5} where the factor 7/8 takes into account the difference between the Fermi and Bose statistics; g, is the total number of light d.o.f. (m « T), and we have also considered the possibility that particle species 7 (bosons or fermions) have an equilibrium distribution at a temperature 7; different from that of photons, as happens for example when a given relativistic species decouples from the thermal bath, as we will discuss later. This number, g,, strongly depends on the temperature of the universe, since as it expands and cools, different particles go out of equilibrium or become non-relativistic (m >> T) and thus become exponentially suppressed from that moment on. A plot of the time evolution of g,(7T’) can be seen in Fig. 7.
Fig. 7: the light degrees of freedom g, and g.5 as a function of the temperature of the universe. From Ref. [[[5} where the factor 7/8 takes into account the difference between the Fermi and Bose statistics; g, is the total number of light d.o.f. (m « T), and we have also considered the possibility that particle species 7 (bosons or fermions) have an equilibrium distribution at a temperature 7; different from that of photons, as happens for example when a given relativistic species decouples from the thermal bath, as we will discuss later. This number, g,, strongly depends on the temperature of the universe, since as it expands and cools, different particles go out of equilibrium or become non-relativistic (m >> T) and thus become exponentially suppressed from that moment on. A plot of the time evolution of g,(7T’) can be seen in Fig. 7.
Fig. 9: The Cosmic Microwave Background Spectrum seen by the FIRAS instrument on COBE. The left panel corresponds to the monopole spectrum, T) = 2.725 + 0.002 K, where the error bars are smaller than the line width. The right panel shows the dipole spectrum, 6T, = 3.372 + 0.014 mK. From Ref. [27). where a = 1/137.036 is the dimensionless electromagnetic coupling constant. The mean free path o: photons 2, in such a plasma can be estimated from the photon interaction rate, A; oT, = neo. Fo temperatures above a few eV, the mean free path is much smaller that the causal horizon at that time anc photons suffer multiple scattering: the plasma is like a dense fog. Photons will decouple from the plasmé when their interaction rate cannot keep up with the expansion of the universe and the mean free path becomes larger than the horizon size: the universe becomes transparent. We can estimate this momen by evaluating [, = H at photon decoupling. Using n. = X-nny, one can compute the decouplinc temperature as Tyj.. = 0.26 eV, and the corresponding redshift as 1 + zg.. ~ 1100. Recently, WMAE measured this redshift to be 1 + zgec ~ 1089 + 1 [20]. This redshift defines the so called last scatterinc surface, when photons last scattered off protons and electrons and travelled freely ever since. Thi: decoupling occurred when the universe was approximately taco = 1.5 x 10° (Qyh?)~!/? ~ 380, 006 years old.
Fig. 9: The Cosmic Microwave Background Spectrum seen by the FIRAS instrument on COBE. The left panel corresponds to the monopole spectrum, T) = 2.725 + 0.002 K, where the error bars are smaller than the line width. The right panel shows the dipole spectrum, 6T, = 3.372 + 0.014 mK. From Ref. [27). where a = 1/137.036 is the dimensionless electromagnetic coupling constant. The mean free path o: photons 2, in such a plasma can be estimated from the photon interaction rate, A; oT, = neo. Fo temperatures above a few eV, the mean free path is much smaller that the causal horizon at that time anc photons suffer multiple scattering: the plasma is like a dense fog. Photons will decouple from the plasmé when their interaction rate cannot keep up with the expansion of the universe and the mean free path becomes larger than the horizon size: the universe becomes transparent. We can estimate this momen by evaluating [, = H at photon decoupling. Using n. = X-nny, one can compute the decouplinc temperature as Tyj.. = 0.26 eV, and the corresponding redshift as 1 + zg.. ~ 1100. Recently, WMAE measured this redshift to be 1 + zgec ~ 1089 + 1 [20]. This redshift defines the so called last scatterinc surface, when photons last scattered off protons and electrons and travelled freely ever since. Thi: decoupling occurred when the universe was approximately taco = 1.5 x 10° (Qyh?)~!/? ~ 380, 006 years old.
Fig. 10: The Cosmic Microwave Background Spectrum seen by the DMR instrument on COBE. The top figure corresponds to the monopole, T) = 2.725 + 0.002 K. The middle figure shows the dipole, 67, = 3.372 + 0.014 mK, and the lower figure shows the quadrupole and higher multipoles, 5T2 = 18 + 2 pK. The central region corresponds to foreground by the galaxy. From Ref. [23].
Fig. 10: The Cosmic Microwave Background Spectrum seen by the DMR instrument on COBE. The top figure corresponds to the monopole, T) = 2.725 + 0.002 K. The middle figure shows the dipole, 67, = 3.372 + 0.014 mK, and the lower figure shows the quadrupole and higher multipoles, 5T2 = 18 + 2 pK. The central region corresponds to foreground by the galaxy. From Ref. [23].
Fig. 11: The IRAS Point Source Catalog redshift survey contains some 15,000 galaxies, covering over 83% of the sky up to redshifts of z < 0.05. We show here the projection of the galaxy distribution in galactic coordinates. From Ref. (27).
Fig. 11: The IRAS Point Source Catalog redshift survey contains some 15,000 galaxies, covering over 83% of the sky up to redshifts of z < 0.05. We show here the projection of the galaxy distribution in galactic coordinates. From Ref. (27).
in the Einstein-de Sitter limit (w = p/p = 1/3 and 0, for radiation and matter, respectively). There are slight deviations for a >> deq, if Qu, A 1 or Qa F O, but we will not be concemed with them here. The important observation is that, since the density contrast at last scattering is of order 5 ~ 107°, and the scale factor has grown since then only a factor zac. ~ 10°, one would expect a density contrast today of order 6) ~ 1077. Instead, we observe structures like galaxies, where 6 ~ 10°. So how can this be possible? The microwave background shows anisotropies due to fluctuations in the baryonic matter component only (to which photons couple, electromagnetically). If there is an additional matter component that only couples through very weak interactions, fluctuations in that component could grow as soon as it decoupled from the plasma, well before photons decoupled from baryons. The reason why baryonic inhomogeneities cannot grow is because of photon pressure: as baryons collapse towards denser regions, radiation pressure eventually halts the contraction and sets up acoustic oscillations in the plasma that prevent the growth of perturbations, until photon decoupling. On the other hand, a weakly interacting cold dark matter component could start gravitational collapse much earlier, even before matter-radiation equality, and thus reach the density contrast amplitudes observed today. The resolution of this mismatch is one of the strongest arguments for the existence of a weakly interacting cold dark matter component of the universe. Fig. 12: The power spectrum for cold dark matter (CDM), tilted cold dark matter (TCDM), hot dark matter (HDM), and mixed hot plus cold dark matter (MDM), normalized to COBE, for large-scale structure formation. From Ref. [28].
in the Einstein-de Sitter limit (w = p/p = 1/3 and 0, for radiation and matter, respectively). There are slight deviations for a >> deq, if Qu, A 1 or Qa F O, but we will not be concemed with them here. The important observation is that, since the density contrast at last scattering is of order 5 ~ 107°, and the scale factor has grown since then only a factor zac. ~ 10°, one would expect a density contrast today of order 6) ~ 1077. Instead, we observe structures like galaxies, where 6 ~ 10°. So how can this be possible? The microwave background shows anisotropies due to fluctuations in the baryonic matter component only (to which photons couple, electromagnetically). If there is an additional matter component that only couples through very weak interactions, fluctuations in that component could grow as soon as it decoupled from the plasma, well before photons decoupled from baryons. The reason why baryonic inhomogeneities cannot grow is because of photon pressure: as baryons collapse towards denser regions, radiation pressure eventually halts the contraction and sets up acoustic oscillations in the plasma that prevent the growth of perturbations, until photon decoupling. On the other hand, a weakly interacting cold dark matter component could start gravitational collapse much earlier, even before matter-radiation equality, and thus reach the density contrast amplitudes observed today. The resolution of this mismatch is one of the strongest arguments for the existence of a weakly interacting cold dark matter component of the universe. Fig. 12: The power spectrum for cold dark matter (CDM), tilted cold dark matter (TCDM), hot dark matter (HDM), and mixed hot plus cold dark matter (MDM), normalized to COBE, for large-scale structure formation. From Ref. [28].
Fig. 13: The Coma cluster of galaxies, seen here in an optical image (left) and an X-ray image (right), taken by the recently launched Chandra X-ray Observatory. From Ref. [34].
Fig. 13: The Coma cluster of galaxies, seen here in an optical image (left) and an X-ray image (right), taken by the recently launched Chandra X-ray Observatory. From Ref. [34].
Fig. 14: The rotation curves of several hundred galaxies. Upper panel: As a function of their radii in kpc. Middle panel: The central 5 kpc. Lower panel: As a function of scale radius.
Fig. 14: The rotation curves of several hundred galaxies. Upper panel: As a function of their radii in kpc. Middle panel: The central 5 kpc. Lower panel: As a function of scale radius.
Fig. 15: The 2 degree Field Galaxy Redshift Survey contains some 250,000 galaxies, covering a large fraction of the sky up to redshifts of z < 0.25. From Ref. [42].
Fig. 15: The 2 degree Field Galaxy Redshift Survey contains some 250,000 galaxies, covering a large fraction of the sky up to redshifts of z < 0.25. From Ref. [42].
Fig. 16: The measured power spectrum P(k) as a function of wavenumber k. From observations of the Sloan Digital Sky Survey, CMB anisotropies, cluster abundance, gravitational lensing and Lyman-a forest. From Ref. [43}.
Fig. 16: The measured power spectrum P(k) as a function of wavenumber k. From observations of the Sloan Digital Sky Survey, CMB anisotropies, cluster abundance, gravitational lensing and Lyman-a forest. From Ref. [43}.
Fig. 17: The observed cosmic matter components as functions of the Hubble expansion parameter. The luminous matter component is given by 0.002 < Qium < 0.006; the galactic halo component is the horizontal band, 0.03 < Qhaio < 0.05, crossing the baryonic component from BBN, 0g h? = 0.0244 + 0.0024; and the dynamical mass component from large scale structure analysis is given by Qa, = 0.3 + 0.1. Note that in the range Hp = 70 + 7 km/s/Mpe, there are three dark matter problems, see the text. From Ref. [44].
Fig. 17: The observed cosmic matter components as functions of the Hubble expansion parameter. The luminous matter component is given by 0.002 < Qium < 0.006; the galactic halo component is the horizontal band, 0.03 < Qhaio < 0.05, crossing the baryonic component from BBN, 0g h? = 0.0244 + 0.0024; and the dynamical mass component from large scale structure analysis is given by Qa, = 0.3 + 0.1. Note that in the range Hp = 70 + 7 km/s/Mpe, there are three dark matter problems, see the text. From Ref. [44].
Fig. 18: Different determinations of Qa, as a function of distance, from various sources: 1. peculiar velocities; 2. weak gravitacional lensing; 3. shear autocorrelation function; 4. local group of galaxies; 5. baryon mass fraction; 6. cluster mass function; 7. virgocentric flow; 8. mean relative velocities; 9. redshift space distortions; 10. mass power spectrum; 11. integrated Sachs-Wolfe effect; 12. angular diameter distance: SNe; 13. cluster baryon fraction. While a few years ago the dispersion among observed values was huge and strongly dependent on scale, at present the observed value of the matter density parameter t 0.07 (95% c.l.) and is essentially independent on scale, from 100 kpc to 5000 falls well within a narrow range, Qar = 0.25 4 Mpc. Adapted from Ref. (45).
Fig. 18: Different determinations of Qa, as a function of distance, from various sources: 1. peculiar velocities; 2. weak gravitacional lensing; 3. shear autocorrelation function; 4. local group of galaxies; 5. baryon mass fraction; 6. cluster mass function; 7. virgocentric flow; 8. mean relative velocities; 9. redshift space distortions; 10. mass power spectrum; 11. integrated Sachs-Wolfe effect; 12. angular diameter distance: SNe; 13. cluster baryon fraction. While a few years ago the dispersion among observed values was huge and strongly dependent on scale, at present the observed value of the matter density parameter t 0.07 (95% c.l.) and is essentially independent on scale, from 100 kpc to 5000 falls well within a narrow range, Qar = 0.25 4 Mpc. Adapted from Ref. (45).
Fig. 19: The neutrino parameter space, mixing angle against Am”, including the results from the different solar and atmospheric neutrino oscillation experiments. Note the threshold of cosmologically important masses, cosmologically detectable neutrinos (by CMB and LSS observations), and cosmologically excluded range of masses. Adapted from Refs. [46] and [9T).
Fig. 19: The neutrino parameter space, mixing angle against Am”, including the results from the different solar and atmospheric neutrino oscillation experiments. Note the threshold of cosmologically important masses, cosmologically detectable neutrinos (by CMB and LSS observations), and cosmologically excluded range of masses. Adapted from Refs. [46] and [9T).
Fig. 20: The annual-modulation signal accumulated over 7 years is consistent with a neutralino of mass of m, = 59 +}, GeV and an nmtan anna cantinn nf ¢. 7 pnt0.4 — 1n—-6 nh annnawiine tra DAMA Brnm Daft fe
Fig. 20: The annual-modulation signal accumulated over 7 years is consistent with a neutralino of mass of m, = 59 +}, GeV and an nmtan anna cantinn nf ¢. 7 pnt0.4 — 1n—-6 nh annnawiine tra DAMA Brnm Daft fe
Fig. 21: Exclusion range for the spin-independent WIMP scattering cross section per nucleon from the Nal experiments and the Ge detectors. The blue lines come from the CDMS experiment, which exclude the DAMA region at more than 3 sigma. Also shown in yellow and red is the range of expected counting rates for neutralinos in the MSSM. From Ref. (53).
Fig. 21: Exclusion range for the spin-independent WIMP scattering cross section per nucleon from the Nal experiments and the Ge detectors. The blue lines come from the CDMS experiment, which exclude the DAMA region at more than 3 sigma. Also shown in yellow and red is the range of expected counting rates for neutralinos in the MSSM. From Ref. (53).
Fig. 22: The recent estimates of the age of the universe and that of the oldest objects in our galaxy. The last three points correspond to the combined analysis of 8 different measurements, for h = 0.64, 0.68 and 7.2, which indicates a relatively weak dependence on h. The age of the Sun is accurately known and is included for reference. Error bars indicate 1c limits. The averages of the ages of the Galactic Halo and Disk are shaded in gray. Note that there isn’t a single age estimate more than 2o away from the average. The result to > tga: is logically inevitable, but the standard EdS model does not satisfy this unless h < 0.55. From Ref. [63]. vations have been made with CCDs, and since refinements to stellar evolution models, including opaci- ties, consideration of mixing, and different chemical abundances have been incorporated [[62). From the theory side, uncertainties in globular cluster ages come from uncertainties in convection models, opac- ities, and nuclear reaction rates. From the observational side, uncertainties arise due to corrections for dust and chemical composition. However, the dominant source of systematic errors in the globular clus- ter age is the uncertainty in the cluster distances. Fortunately, the Hipparcos satellite recently provided geometric parallax measurements for many nearby old stars with low metallicity, typical of glubular clus- ters, thus allowing for a new calibration of the ages of stars in globular clusters, leading to a downward revision to 10 — 13 Gyr [62]. Moreover, there were very few stars in the Hipparcos catalog with both small parallax erros and low metal abundance. Hence, an increase in the sample size could be critical in reducing the statatistical uncertaintites for the calibration of the globular cluster ages. There are already proposed two new parallax satellites, NASA’s Space Interferometry Mission (SIM) and ESA’s mission, called GAIA, that will give 2 or 3 orders of magnitude more accurate parallaxes than Hipparcos, down to fainter magnitude limits, for several orders of magnitude more stars. Until larger samples are avail- able, however, distance errors are likely to be the largest source of systematic uncertainty to the globular cluster age [29].
Fig. 22: The recent estimates of the age of the universe and that of the oldest objects in our galaxy. The last three points correspond to the combined analysis of 8 different measurements, for h = 0.64, 0.68 and 7.2, which indicates a relatively weak dependence on h. The age of the Sun is accurately known and is included for reference. Error bars indicate 1c limits. The averages of the ages of the Galactic Halo and Disk are shaded in gray. Note that there isn’t a single age estimate more than 2o away from the average. The result to > tga: is logically inevitable, but the standard EdS model does not satisfy this unless h < 0.55. From Ref. [63]. vations have been made with CCDs, and since refinements to stellar evolution models, including opaci- ties, consideration of mixing, and different chemical abundances have been incorporated [[62). From the theory side, uncertainties in globular cluster ages come from uncertainties in convection models, opac- ities, and nuclear reaction rates. From the observational side, uncertainties arise due to corrections for dust and chemical composition. However, the dominant source of systematic errors in the globular clus- ter age is the uncertainty in the cluster distances. Fortunately, the Hipparcos satellite recently provided geometric parallax measurements for many nearby old stars with low metallicity, typical of glubular clus- ters, thus allowing for a new calibration of the ages of stars in globular clusters, leading to a downward revision to 10 — 13 Gyr [62]. Moreover, there were very few stars in the Hipparcos catalog with both small parallax erros and low metal abundance. Hence, an increase in the sample size could be critical in reducing the statatistical uncertaintites for the calibration of the globular cluster ages. There are already proposed two new parallax satellites, NASA’s Space Interferometry Mission (SIM) and ESA’s mission, called GAIA, that will give 2 or 3 orders of magnitude more accurate parallaxes than Hipparcos, down to fainter magnitude limits, for several orders of magnitude more stars. Until larger samples are avail- able, however, distance errors are likely to be the largest source of systematic uncertainty to the globular cluster age [29].
result is shown in Fig. [22] compared to other recent determinations. The best fit value for the age of the universe is, according to this analysis, tg) = 13.4 + 1.6 Gyr, about a billion years younger than other recent estimates [[63). Fig. 23: The anisotropies of the microwave background measured by the WMAP satellite with 10 arcminute resolution. It shows the intrinsic CMB anisotropies at the level of a few parts in 10°. The galactic foreground has been properly subtracted. The amount of information contained in this map is enough to determine most of the cosmological parameters to few percent accuracy. From Ref. [20].
result is shown in Fig. [22] compared to other recent determinations. The best fit value for the age of the universe is, according to this analysis, tg) = 13.4 + 1.6 Gyr, about a billion years younger than other recent estimates [[63). Fig. 23: The anisotropies of the microwave background measured by the WMAP satellite with 10 arcminute resolution. It shows the intrinsic CMB anisotropies at the level of a few parts in 10°. The galactic foreground has been properly subtracted. The amount of information contained in this map is enough to determine most of the cosmological parameters to few percent accuracy. From Ref. [20].
Fig. 24: The Angular Power Spectrum of CMB temperature anisotropies, compared with the cross-correlation of temperature- polarization anisotropies. From Ref. (20).
Fig. 24: The Angular Power Spectrum of CMB temperature anisotropies, compared with the cross-correlation of temperature- polarization anisotropies. From Ref. (20).
Table 2: The parameters of the standard cosmological model. The standard model of cosmology has about 20 different parameters, needed to describe the background space-time, the matter content and the spectrum of metric perturbations. We include here the present range of the most relevant parameters (with 1c errors), as recently determined by WMAP, and the error with which the Planck satellite will be able to determine them in the near future. The rate of expansion is written in units of H = 100h km/s/Mpc. H = 100h km/s/Mpc. From the observations of the CMB anisotropies it is possible to determine most of the parame- ters of the Standard Cosmological Model with few percent accuracy, see Table 2. However, there are many degeneracies between parameters and it is difficult to disentangle one from another. For instance, as mentioned above, the first peak in the photon distribution corresponds to overdensities that have un- dergone half an oscillation, that is, a compression, and appear at a scale associated with the size of the horizon at last scattering, about 1° projected in the sky today. Since photons scatter off baryons, they will also feel the acoustic wave and create a peak in the correlation function. The height of the peak is proportional to the amount of baryons: the larger the baryon content of the universe, the higher the peak. The position of the peak in the power spectrum depends on the geometrical size of the particle horizon at last scattering. Since photons travel along geodesics, the projected size of the causal horizon at decoupling depends on whether the universe is flat, open or closed. In a flat universe the geodesics are straight lines and, by looking at the angular scale of the first acoustic peak, we would be measuring the actual size of the horizon at last scattering. In an open universe, the geodesics are inward-curved tre- jectories, and therefore the projected size on the sky appears smaller. In this case, the first acoustic peak should occur at higher multipoles or smaller angular scales. On the other hand, for a closed universe, the first peak occurs at smaller multipoles or larger angular scales. The dependence of the position of
Table 2: The parameters of the standard cosmological model. The standard model of cosmology has about 20 different parameters, needed to describe the background space-time, the matter content and the spectrum of metric perturbations. We include here the present range of the most relevant parameters (with 1c errors), as recently determined by WMAP, and the error with which the Planck satellite will be able to determine them in the near future. The rate of expansion is written in units of H = 100h km/s/Mpc. H = 100h km/s/Mpc. From the observations of the CMB anisotropies it is possible to determine most of the parame- ters of the Standard Cosmological Model with few percent accuracy, see Table 2. However, there are many degeneracies between parameters and it is difficult to disentangle one from another. For instance, as mentioned above, the first peak in the photon distribution corresponds to overdensities that have un- dergone half an oscillation, that is, a compression, and appear at a scale associated with the size of the horizon at last scattering, about 1° projected in the sky today. Since photons scatter off baryons, they will also feel the acoustic wave and create a peak in the correlation function. The height of the peak is proportional to the amount of baryons: the larger the baryon content of the universe, the higher the peak. The position of the peak in the power spectrum depends on the geometrical size of the particle horizon at last scattering. Since photons travel along geodesics, the projected size of the causal horizon at decoupling depends on whether the universe is flat, open or closed. In a flat universe the geodesics are straight lines and, by looking at the angular scale of the first acoustic peak, we would be measuring the actual size of the horizon at last scattering. In an open universe, the geodesics are inward-curved tre- jectories, and therefore the projected size on the sky appears smaller. In this case, the first acoustic peak should occur at higher multipoles or smaller angular scales. On the other hand, for a closed universe, the first peak occurs at smaller multipoles or larger angular scales. The dependence of the position of
Fig. 25: The (Qaz, Qa) plane with the present data set of cosmological observations — the acceleration of the universe, the large scale structure and the CMB anisotropies — as well as the future determinations by SNAP and Planck of the fundamental parameters which define our Standard Model of Cosmology. the first acoustic peak on the spatial curvature can be approximately given by [peak ~ 2200) 1/2 where 2 = OM+QA = 1—Ox. Present observations by WMAP and other experiments give Q) = 1.00+0.02 it one standard deviation (20).
Fig. 25: The (Qaz, Qa) plane with the present data set of cosmological observations — the acceleration of the universe, the large scale structure and the CMB anisotropies — as well as the future determinations by SNAP and Planck of the fundamental parameters which define our Standard Model of Cosmology. the first acoustic peak on the spatial curvature can be approximately given by [peak ~ 2200) 1/2 where 2 = OM+QA = 1—Ox. Present observations by WMAP and other experiments give Q) = 1.00+0.02 it one standard deviation (20).
Fig. 26: Perhaps the most acute problem of the Big Bang theory is explaining the extraordinary homogeneity and isotropy of the microwave background, see Fig.[I0] At the time of decoupling, the volume that gave rise to our present universe contained many causally disconnected regions (top figure). Today we observe a blackbody spectrum of photons coming from those regions and they appear to have the same temperature, T, = T», to one part in 10°. Why is the universe so homogeneous? This constitutes the so-called horizon problem, which is spectacularly solved by inflation. From Ref. 70}.
Fig. 26: Perhaps the most acute problem of the Big Bang theory is explaining the extraordinary homogeneity and isotropy of the microwave background, see Fig.[I0] At the time of decoupling, the volume that gave rise to our present universe contained many causally disconnected regions (top figure). Today we observe a blackbody spectrum of photons coming from those regions and they appear to have the same temperature, T, = T», to one part in 10°. Why is the universe so homogeneous? This constitutes the so-called horizon problem, which is spectacularly solved by inflation. From Ref. 70}.
Fig. 27: The inflaton field can be represented as a ball rolling down a hill. During inflation, the energy density is approximately constant, driving the tremendous expansion of the universe. When the ball starts to oscillate around the bottom of the hill, inflation ends and the inflaton energy decays into particles. In certain cases, the coherent oscillations of the inflaton could generate a resonant production of particles which soon thermalize, reheating the universe. From Ref. [[70}.
Fig. 27: The inflaton field can be represented as a ball rolling down a hill. During inflation, the energy density is approximately constant, driving the tremendous expansion of the universe. When the ball starts to oscillate around the bottom of the hill, inflation ends and the inflaton energy decays into particles. In certain cases, the coherent oscillations of the inflaton could generate a resonant production of particles which soon thermalize, reheating the universe. From Ref. [[70}.
Fig. 28: The exponential expansion during inflation made the radius of curvature of the universe so large that our observable patch of the universe today appears essentialy flat, analogous (in three dimensions) to how the surface of a balloon appears flatter and flatter as we inflate it to enormous sizes. This is a crucial prediction of cosmological inflation that will be tested to extraordinary accuracy in the next few years. From Ref. [[74][70). ‘ig. 28: The exponential expansion during inflation made the radius of curvature of the universe so large that our observable extraordinary accuracy in the next few years. From Ref. [//4]//0].
Fig. 28: The exponential expansion during inflation made the radius of curvature of the universe so large that our observable patch of the universe today appears essentialy flat, analogous (in three dimensions) to how the surface of a balloon appears flatter and flatter as we inflate it to enormous sizes. This is a crucial prediction of cosmological inflation that will be tested to extraordinary accuracy in the next few years. From Ref. [[74][70). ‘ig. 28: The exponential expansion during inflation made the radius of curvature of the universe so large that our observable extraordinary accuracy in the next few years. From Ref. [//4]//0].
That is, the universe is spatially flat (i.e. Euclidean), within 2% uncertainty, which is much better than we could ever do before. Fig. 29: The dependence of CMB anisotropies and LSS power spectrum on the sum of the mass of all neutrino species. The blue(red) data corresponds to WMA P(Boomerang, etc.) and SDSS(2dFGRS), for the CMB and LSS respectively.
That is, the universe is spatially flat (i.e. Euclidean), within 2% uncertainty, which is much better than we could ever do before. Fig. 29: The dependence of CMB anisotropies and LSS power spectrum on the sum of the mass of all neutrino species. The blue(red) data corresponds to WMA P(Boomerang, etc.) and SDSS(2dFGRS), for the CMB and LSS respectively.
ably the most important objective of the future satellites (beyond WMAP) will be the measurement of the CMB polarization anisotropies, discovered by DASI in November 2002 [98], and confirmed a few months later by WMAP with greater accuracy [20], see Fig. 24. These anisotropies were predicted by models of structure formation and indeed found at the level of microKelvin sensitivities, where the new satellites were aiming at. The complementary information contained in the polarization anisotropies already provides much more stringent constraints on the cosmological parameters than from the temper- ature anisotropies alone. However, in the future, Planck and CMB pol will have much better sensitivities. In particular, the curl-curl component of the polarization power spectra is nowadays the only means we have to determine the tensor (gravitational wave) contribution to the metric perturbations responsible for temperature anisotropies, see Fig. BO] If such a component is found, one could constraint very precisely the model of inflation from its spectral properties, specially the tilt [9T). Fig. 30: Theoretical predictions for the four non-zero CMB temperature- polarization spectra as a function of multipole moment, together with the expectations from Planck. From Ref. (92).
ably the most important objective of the future satellites (beyond WMAP) will be the measurement of the CMB polarization anisotropies, discovered by DASI in November 2002 [98], and confirmed a few months later by WMAP with greater accuracy [20], see Fig. 24. These anisotropies were predicted by models of structure formation and indeed found at the level of microKelvin sensitivities, where the new satellites were aiming at. The complementary information contained in the polarization anisotropies already provides much more stringent constraints on the cosmological parameters than from the temper- ature anisotropies alone. However, in the future, Planck and CMB pol will have much better sensitivities. In particular, the curl-curl component of the polarization power spectra is nowadays the only means we have to determine the tensor (gravitational wave) contribution to the metric perturbations responsible for temperature anisotropies, see Fig. BO] If such a component is found, one could constraint very precisely the model of inflation from its spectral properties, specially the tilt [9T). Fig. 30: Theoretical predictions for the four non-zero CMB temperature- polarization spectra as a function of multipole moment, together with the expectations from Planck. From Ref. (92).
Fig. 31: The CDM power spectrum P(k) as a function of wavenumber k, in logarithmic scale, normalized to the local abun- dance of galaxy clusters, for an Einstein-de Sitter universe with h = 0.5. The solid (dashed) curve shows the linear (non-linear) power spectrum. While the linear power spectrum falls off like k~*, the non-linear power-spectrum illustrates the increased power on small scales due to non-linear effects, at the expense of the large-scale structures. From Ref. [41]. We see that the behaviour estimated in Eq. (243) is roughly correct, although the break at k = keg is not at all sharp, see Fig. [31] The transfer function, which encodes the soltion to linear equations, ceases to be valid when the density contrast becomes of order 1. After that, the highly nonlinear phenomenon of gravitational collapse takes place, see Fig. [BT] Fig. 31: The CDM power spectrum P(k) as a function of wavenumber k, in logarithmic scale, normalized to the local abun-
Fig. 31: The CDM power spectrum P(k) as a function of wavenumber k, in logarithmic scale, normalized to the local abun- dance of galaxy clusters, for an Einstein-de Sitter universe with h = 0.5. The solid (dashed) curve shows the linear (non-linear) power spectrum. While the linear power spectrum falls off like k~*, the non-linear power-spectrum illustrates the increased power on small scales due to non-linear effects, at the expense of the large-scale structures. From Ref. [41]. We see that the behaviour estimated in Eq. (243) is roughly correct, although the break at k = keg is not at all sharp, see Fig. [31] The transfer function, which encodes the soltion to linear equations, ceases to be valid when the density contrast becomes of order 1. After that, the highly nonlinear phenomenon of gravitational collapse takes place, see Fig. [BT] Fig. 31: The CDM power spectrum P(k) as a function of wavenumber k, in logarithmic scale, normalized to the local abun-
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