The next generation of telescopes will usher in a new era of precision cosmology capable of deter... more The next generation of telescopes will usher in a new era of precision cosmology capable of determining key parameters of a cosmological model to percent level and beyond. For this to be effective, the theoretical model must be understood to at least the same level of precision. A range of subtle physical spacetime effects remain to be explored theoretically, for example, the effect of backreaction on cosmological observables. A good understanding of this effect is paramount given that it is a consequence of any space-time theory of gravity. We provide a comprehensive study of this effect from the perspective of geometric averaging on a hyper-surface and averaging on the celestial sphere. We concentrate on Friedmann-Lemaitre-Robertson-Walker spacetime with small perturbation up to non-linear order. This enables us to quantify by how much this effect could change the standard model interpretation of the universe. We study in great detail key parameters of the standard model, Hubble rate, deceleration parameter and area distance. We find that the Hubble rate depends on the choice of definition of the Hubble rate and the spatial surface on which the average is performed. Within the ΛCDM model, the backreaction effect on the background Hubble rate is of order 1% at a scale of 100 Mpc, and much less on larger scales. We find that for the deceleration parameter adapted to observation, the perturbation theory gives divergent answers in the UV and corrections to the background are of order unity or more depending on the choice of UV cutoff. For the area distance, we identify a range of new lensing effects, which include: double-integrated and nonlinear integrated Sach-Wolfe contributions, transverse Doppler effects in redshift space distortions, lensing from the induced vector mode and gravitational wave backgrounds, in addition to lensing from the secondorder potential and we also identify a new double-coupling between the density fluctuations integrated along the line of sight, and gradients in the density fluctuations coupled to transverse velocities along the line of sight. We conclude that the precision cosmology would be unsuccessful without the effect of backreaction being properly taking into account in parameter estimation. Also we need to rethink our theoretical approach to sub-horizon universe because un-renormalized perturbation theory appear not to be working. I would like to thank Camille Bonvin and Ruth Durrer for useful technical discussions on area distance in cosmology. I appreciate a detailed email clarifying the technical subtleties associated with switching of averaging hyper-surface by Giovanni Marozzi. I would also like to thank Gabriele Veneziano and his collaborators for comments on the first draft of the area distance paper. I would like to thank Alex Weigand and Dominik Schwarz for comments on the fitting formula for the averaged Hubble rate and the relationship with their work. I appreciate discussion with Albert Stebbins on constructing observable quantities. I also owe a special thanks to my office mate and friend Sean February for discussion and proofreading part of the thesis. I am grateful to Cyril Pitrou and JP Uzan for discussions on many aspects of this work and other unpublished works. I am very grateful to Sean Hartnoll for saving me from self-destruction during my Msc studies and after. I am highly indebted to Astrophysics section of department of Physics Oxford University for hospitality during the time I spent with them. I appreciate every special assistance given to me especially by Pedro Ferreira , Tim Clifton, Phil Bull, Sarah White, Krzysztof Bolejko, Edward Macaulay, and all the graduate students in the group. I would like to thank in a special way my supervisors: Chris Clarkson and George F. R. Ellis for both academic and personal guidance and assistance. I owe a special thanks to George for reading through every paragraph of this thesis. I am very grateful for this. Most of the computations here were done with the help of the tensor algebra package xPert/xAct [1] and xPand which I developed in collaboration with Cyril Pitrou and Xavier Roy.
The success of precision cosmology depends not only on accurate observations, but also on the the... more The success of precision cosmology depends not only on accurate observations, but also on the theoretical model - which must be understood to at least the same level of precision. Subtle relativistic effects can lead to biased measurements if they are neglected. One such effect gives a systematic shift in the distance-redshift relation away from its background value, due to the non- linear relativistic conservation of total photon flux. We also show directly how this shift follows from a fully relativistic analysis of the geodesic deviation equation. We derive the expectation value of the shift using second-order perturbations about a concordance background, and show that the distance to last scattering is increased by 1%. We argue that neglecting this shift could lead to a significant bias in the background cosmological parameters, because it alters the meaning of the background model. A naive adjustment of CMB parameter estimation if this shift is really a correction to the backgr...
It has recently been shown that second-order corrections to the background distance-redshift rela... more It has recently been shown that second-order corrections to the background distance-redshift relation can build up significantly at large redshifts, due to an aggregation of gravitational lensing events. This shifts the expectation value of the distance to the CMB by 1%. In this paper we show that this shift is already properly accounted for in standard CMB analyses. We clarify the role that the area distance to the CMB plays in the presence of second-order lensing corrections.
Smoothing over structures in general relativity leads to a renormalisation of the background, and... more Smoothing over structures in general relativity leads to a renormalisation of the background, and potentially many other effects which are poorly understood. Observables such as the distance-redshift relation when averaged on the sky do not necessarily yield the same smooth model which arises when performing spatial averages. These issues are thought to be of technical interest only in the standard model of cosmology, giving only tiny corrections. However, when we try to calculate observable quantities such as the all-sky average of the distance-redshift relation, we find that perturbation theory delivers divergent answers in the UV and corrections to the background of order unity. There are further problems. Second-order perturbations are the same size as first-order, and fourth-order at least the same as second, and possibly much larger, owing to the divergences. Much hinges on a coincidental balance of 2 numbers: the primordial power, and the ratio between the comoving Hubble sca...
Journal of Cosmology and Astroparticle Physics, 2021
Post-reionisation 21cm intensity mapping experiments target the spectral line of neutral hydrogen... more Post-reionisation 21cm intensity mapping experiments target the spectral line of neutral hydrogen (HI) resident in dark matter haloes. According to the halo model, these discrete haloes trace the continuous dark matter density field down to a certain scale, which is dependent on the halo physical size. The halo physical size defines an exclusion region which leaves imprints on the statistical properties of HI. We show how the effect of exclusion due to the finite halo size impacts the HI power spectrum, with the physical boundary of the host halo given by the splashback radius. Most importantly, we show that the white noise-like feature that appears in the zero-momentum limit of the power spectrum is exactly cancelled when the finite halo size is taken into consideration. This cancellation in fact applies to all tracers of dark matter density field, including galaxies. Furthermore, we show that the exclusion due to finite halo size leads to a sub-Poissonian noise signature on large ...
The Fourier-space galaxy bispectrum is complex, with the imaginary part arising from leading-orde... more The Fourier-space galaxy bispectrum is complex, with the imaginary part arising from leading-order relativistic corrections, due to Doppler, gravitational redshift and related line-of-sight effects in redshift space. The detection of the imaginary part of the bispectrum is potentially a smoking gun signal of relativistic contributions. We investigate whether next-generation spectroscopic surveys could make such a detection. For a Stage IV spectroscopic Hα survey similar to Euclid, we find that the cumulative signal to noise of this relativistic signature is O(10). Long-mode relativistic effects couple to short-mode Newtonian effects in the galaxy bispectrum, but not in the galaxy power spectrum. This is the basis for detectability of relativistic effects in the bispectrum of a single galaxy survey, whereas the power spectrum requires multiple galaxy surveys to detect the corresponding signal.
Smoothing over structures in general relativity leads to a renormalisation of the background, and... more Smoothing over structures in general relativity leads to a renormalisation of the background, and potentially many other effects which are poorly understood. Observables such as the distance-redshift relation when averaged on the sky do not necessarily yield the same smooth model which arises when performing spatial averages. These issues are thought to be of technical interest only in the standard model of cosmology, giving only tiny corrections. However, when we try to calculate observable quantities such as the all-sky average of the distance-redshift relation, we find that perturbation theory delivers divergent answers in the UV and corrections to the background of order unity. There are further problems. Second-order perturbations are the same size as first-order, and fourth-order at least the same as second, and possibly much larger, owing to the divergences. Much hinges on a coincidental balance of 2 numbers: the primordial power, and the ratio between the comoving Hubble scales at matter-radiation equality and today. Consequently, it is far from obvious that backreaction is irrelevant even in the concordance model, however natural it intuitively seems.
Journal of Cosmology and Astroparticle Physics, 2021
Next-generation galaxy and 21cm intensity mapping surveys will rely on a combination of the power... more Next-generation galaxy and 21cm intensity mapping surveys will rely on a combination of the power spectrum and bispectrum for high-precision measurements of primordial non-Gaussianity. In turn, these measurements will allow us to distinguish between various models of inflation. However, precision observations require theoretical precision at least at the same level. We extend the theoretical understanding of the galaxy bispectrum by incorporating a consistent general relativistic model of galaxy bias at second order, in the presence of local primordial non-Gaussianity. The influence of primordial non-Gaussianity on the bispectrum extends beyond the galaxy bias and the dark matter density, due to redshift-space effects. The standard redshift-space distortions at first and second order produce a well-known primordial non-Gaussian imprint on the bispectrum. Relativistic corrections to redshift-space distortions generate new contributions to this primordial non-Gaussian signal, arising ...
Journal of Cosmology and Astroparticle Physics, 2021
One of the cornerstones of general relativity is the equivalence principle. However, the validity... more One of the cornerstones of general relativity is the equivalence principle. However, the validity of the equivalence principle has only been established on solar system scales for standard matter fields; this result cannot be assumed to hold for the non-standard matter fields that dominate the gravitational dynamics on cosmological scales. Here we show how the equivalence principle may be tested on cosmological scales for non-standard matter fields using the odd multipoles of the galaxy cross-power spectrum and bispectrum. This test makes use of the imprint on the galaxy cross-power spectrum and bispectrum by the parity-violating general relativistic deformations of the past-light cone, and assumes that galaxies can be treated as test particles that are made of baryons and cold dark matter. This assumption leads to a non-zero galaxy-baryon relative velocity if the equivalence principle does not hold between baryons and dark matter. We show that the relative velocity can be constrained to be less than 28% of the galaxy velocity using the cross-power spectrum of the HI intensity mapping/Hα galaxy survey and the bispectrum of the Hα galaxy survey.
Journal of Cosmology and Astroparticle Physics, 2021
We investigate the detectability of leading-order relativistic effects in the bispectrum of futur... more We investigate the detectability of leading-order relativistic effects in the bispectrum of future 21cm intensity mapping surveys. The relativistic signal arises from Doppler and other line-of-sight effects in redshift space. In the power spectrum of a single tracer, these effects are suppressed by a factor ℋ2/k2. By contrast, in the bispectrum the relativistic signal couples to short-scale modes, leading to an imaginary contribution that scales as ℋ/k, thus increasing the possibility of detection. Previous work has shown that this relativistic signal is detectable in a Stage IV Hα galaxy survey. We show that the signal is also detectable by next-generation 21cm intensity maps, but typically with a lower signal-to-noise, due to foreground and telescope beam effects.
Journal of Cosmology and Astroparticle Physics, 2020
Above the equality scale the galaxy bispectrum will be a key probe for measuring primordial non-G... more Above the equality scale the galaxy bispectrum will be a key probe for measuring primordial non-Gaussianity which can help differentiate between different inflationary models and other theories of the early universe. On these scales a variety of relativistic effects come into play once the galaxy number-count fluctuation is projected onto our past lightcone. By decomposing the Fourier-space bispectrum into invariant multipoles about the observer's line of sight we examine in detail how the relativistic effects contribute to these. We show how to perform this decomposition analytically, which is significantly faster for subsequent computations. While all multipoles receive a contribution from the relativistic part, odd multipoles arising from the imaginary part of the bispectrum have no Newtonian contribution, making the odd multipoles a smoking gun for a relativistic signature in the bispectrum for single tracers. The dipole and the octopole are significant on equality scales and above where the Newtonian approximation breaks down. This breakdown is further signified by the fact that the even multipoles receive a significant correction on very large scales.
Journal of Cosmology and Astroparticle Physics, 2020
The Fourier galaxy bispectrum is complex, with the imaginary part arising from leading-order rela... more The Fourier galaxy bispectrum is complex, with the imaginary part arising from leading-order relativistic corrections, due to Doppler, gravitational redshift and related lineof-sight effects in redshift space. The detection of the imaginary part of the bispectrum is potentially a smoking gun signal of relativistic contributions. We investigate whether nextgeneration spectroscopic surveys could make such a detection. For a Stage IV spectroscopic Hα survey similar to Euclid, we find that the cumulative signal to noise of this relativistic signature is O(10). Long-mode relativistic effects couple to short-mode Newtonian effects in the galaxy bispectrum, but not in the galaxy power spectrum. This is the basis for detectability of relativistic effects in the bispectrum of a single galaxy survey, whereas the power spectrum requires multiple galaxy surveys to detect the corresponding signal.
Journal of Cosmology and Astroparticle Physics, 2018
Using the consistency relation in Fourier space, we derive the observed galaxy bispectrum from si... more Using the consistency relation in Fourier space, we derive the observed galaxy bispectrum from single-field inflation in the squeezed limit, in which one of the three modes has a wavelength much longer than the other two. This provides a non-trivial check of the full computation of the bispectrum based on second-order cosmological perturbation theory in this limit. We show that gauge modes need to be carefully removed in the second-order cosmological perturbations in order to calculate the observed galaxy bispectrum in the squeezed limit. We then give an estimate of the effective non-Gaussianity due to general-relativistic lightcone effects that could mimic a primordial non-Gaussian signal.
Journal of Cosmology and Astroparticle Physics, 2018
The galaxy bispectrum is affected on equality scales and above by relativistic observational effe... more The galaxy bispectrum is affected on equality scales and above by relativistic observational effects, at linear and nonlinear order. These lightcone effects include local contributions from Doppler and gravitational potential terms, as well as integrated contributions like lensing, together with all the couplings at nonlinear order. We recently presented the correction to the galaxy bispectrum from all local lightcone effects up to second order in perturbations, using a plane-parallel approximation. Here we update our previous result by including the effects from relativistic nonlinear dynamical evolution. We show that these dynamical effects make a significant contribution to the projection effects. I. INTRODUCTION Galaxy counts are distorted due to the fact that we observe on the past lightcone. The Kaiser redshift-space distortion (RSD) effect is well known. Lensing convergence also distorts the number counts. There are further distortions from Doppler, Sachs-Wolfe, ISW and time-delay effects, which are suppressed on sub-equality scales. At nonlinear order, there are couplings amongst all of these projection effects. The full set of relativistic projection effects has been computed at first order by [1-3], and then at second order by [4-8]. The observed galaxy power spectrum at tree level involves only the first-order projection effects. On superequality scales, the relativistic projection effects are similar to the effects of scale-dependent bias, so that these effects need to be taken into account when measuring or constraining primordial non-Gaussianity [9-12]. The observed galaxy bispectrum at tree level involves both first-and second-order projection effects, which on ultralarge scales could also be mistaken for primordial non-Gaussianity. We recently computed the galaxy bispectrum with all local relativistic projection effects, i.e., neglecting terms involving lensing and other line-of-sight integrals. This approximation is imposed on us since, in the early papers of this series, we work in Fourier space (in common with much of the literature on the galaxy bispectrum). In principle it is known how to include the integrated contributions-by working with the relativistic galaxy three-point correlation function or angular harmonic bispectrum. But in practice this is a formidable challenge which has not yet been met. Another approximation that is imposed by a standard Fourier-space analysis is the plane-parallel approximation, which excludes wide-angle correlations. Wideangle correlations would be automatically included in an angular harmonic or three-point correlation analysis that inorporated integrated effects. We plan to include integrated and wide-angle contributions in future papers of this series. Papers I and II provided a compact kernel for easy Fourier-space computations: in Paper I [13] we presented the main results and in Paper II [14] we gave the details behind the main results, and also generalised these results. (See also other computations for special cases in [15-17] and a formalism for the general case in [18].) In this Paper III of the series, we include additional effects (identified in Paper II) to update the general result in Paper II. We do not repeat the general treatment of Paper II, but refer the reader to Paper II for the general discussion, the detailed derivations of key results and their full expressions. For convenience, we include in Appendix A some of the relevant basic formulas and definitions. The expression for the observed galaxy number count contrast at second order [4-8] is extremely long and complicated-even if we omit all terms with integrated contributions. A convenient form in the local case is given in Paper II [14], in the Poisson gauge. In Paper III our focus is on the contributions from the second-order gravitational potentials and the peculiar velocity potential: we used the standard (Newtonian) expressions in Paper II and here we will compute the relativistic corrections. These contributions enter the observed galaxy number contrast as follows
Journal of Cosmology and Astroparticle Physics, 2016
Intensity mapping of the neutral hydrogen brightness temperature promises to provide a threedimen... more Intensity mapping of the neutral hydrogen brightness temperature promises to provide a threedimensional view of the universe on very large scales. Nonlinear effects are typically thought to alter only the small-scale power, but we show how they may bias the extraction of cosmological information contained in the power spectrum on ultra-large scales. For linear perturbations to remain valid on large scales, we need to renormalize perturbations at higher order. In the case of intensity mapping, the second-order contribution to clustering from weak lensing dominates the nonlinear contribution at high redshift. Renormalization modifies the mean brightness temperature and therefore the evolution bias. It also introduces a term that mimics white noise. These effects may influence forecasting analysis on ultra-large scales.
Journal of Cosmology and Astroparticle Physics, 2017
Next-generation galaxy surveys will increasingly rely on the galaxy bispectrum to improve cosmolo... more Next-generation galaxy surveys will increasingly rely on the galaxy bispectrum to improve cosmological constraints, especially on primordial non-Gaussianity. A key theoretical requirement that remains to be developed is the analysis of general relativistic effects on the bispectrum, which arise from observing galaxies on the past lightcone, as well as from relativistic corrections to the dynamics. As an initial step towards a fully relativistic analysis of the galaxy bispectrum, we compute for the first time the local relativistic lightcone effects on the bispectrum, which come from Doppler and gravitational potential contributions. For the galaxy bispectrum, the problem is much more complex than for the power spectrum, since we need the lightcone corrections at second order. Mode-coupling contributions at second order mean that relativistic corrections can be non-negligible at smaller scales than in the case of the power spectrum. In a primordial Gaussian universe, we show that the local lightcone corrections for squeezed shapes at z ∼ 1 mean that the bispectrum can differ from the Newtonian prediction by 10% when the short modes are k (50 Mpc) -1 . These relativistic projection effects, if ignored in the analysis of observations, could be mistaken for primordial non-Gaussianity. For upcoming surveys which probe equality scales and beyond, all relativistic lightcone effects and relativistic dynamical corrections should be included for an accurate measurement of primordial non-Gaussianity.
We consider the entropy associated with the large-scale structure of the Universe in the linear r... more We consider the entropy associated with the large-scale structure of the Universe in the linear regime, where the Universe can be described by a perturbed Friedmann-Lemaître spacetime. In particular, we compare two different definitions proposed in the literature for the entropy using a spatial averaging prescription. For one definition, the entropy of the large-scale structure for a given comoving volume always grows with time, both for a CDM and a ΛCDM model. In particular, while it diverges for a CDM model, it saturates to a constant value in the presence of a cosmological constant. The use of a light-cone averaging prescription in the context of the evaluation of the entropy is also discussed.
Journal of Cosmology and Astroparticle Physics, 2015
It has recently been shown that second-order corrections to the background distance-redshift rela... more It has recently been shown that second-order corrections to the background distance-redshift relation can build up significantly at large redshifts, due to an aggregation of gravitational lensing events. This shifts the expectation value of the distance to the CMB by 1%. In this paper we show that this shift is already properly accounted for in standard CMB analyses. We clarify the role that the area distance to the CMB plays in the presence of second-order lensing corrections.
Journal of Cosmology and Astroparticle Physics, 2015
We show that at second order, ensemble averages of observables and directional averages do not co... more We show that at second order, ensemble averages of observables and directional averages do not commute due to gravitational lensing -observing the same thing in many directions over the sky is not the same as taking an ensemble average. In principle this non-commutativity is significant for a variety of quantities that we often use as observables and can lead to a bias in parameter estimation. We derive the relation between the ensemble average and the directional average of an observable, at second order in perturbation theory. We discuss the relevance of these two types of averages for making predictions of cosmological observables, focusing on observables related to distances and magnitudes. In particular, we show that the ensemble average of the distance in a given observed direction is increased by gravitational lensing, whereas the directional average of the distance is decreased. For a generic observable, there exists a particular function of the observable that is not affected by second-order lensing perturbations. We also show that standard areas have an advantage over standard rulers, and we discuss the subtleties involved in averaging in the case of supernova observations.
The next generation of telescopes will usher in an era of precision cosmology, capable of determi... more The next generation of telescopes will usher in an era of precision cosmology, capable of determining the cosmological model to beyond the percent level. For this to be effective, the theoretical model must be understood to at least the same level of precision. A range of subtle relativistic effects remain to be explored theoretically, and offer the potential for probing general relativity in this new regime. We present the distance-redshift relation to second order in cosmological perturbation theory for a general dark energy model. This relation determines the magnification of sources at high precision, as well as redshift space distortions in the mildly non-linear regime. We identify a range of new lensing effects, including: double-integrated and nonlinear integrated Sach-Wolfe contributions, transverse Doppler effects, lensing from the induced vector mode and gravitational wave backgrounds, in addition to lensing from the second-order potential. Modifications to Doppler lensing from redshift-space distortions are identified. Finally, we find a new double-coupling between the density fluctuations integrated along the line of sight, and gradients in the density fluctuations coupled to transverse velocities along the line of sight. These can be large and thus offer important new probes of gravitational lensing and general relativity. This paper accompanies Paper II, where a comprehensive derivation is given.
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Papers by Obinna Umeh