We calculate two-point functions of scalar fields of mass m and their conjugate momenta at the la... more We calculate two-point functions of scalar fields of mass m and their conjugate momenta at the late-time boundary of de Sitter with Bunch-Davies boundary conditions, in general d + 1 spacetime dimensions. We perform the calculation using the wavefunction picture and using canonical quantization. With the latter one clearly sees how the latetime field and conjugate momentum operators are linear combinations of the normalized late-time operators α N and β N that correspond to unitary irreducible representations of the de Sitter group with well-defined inner products. The two-point functions resulting from these two different methods are equal and we find that both the autocorrelations of α N and β N and their cross correlations contribute to the late-time field and conjugate momentum two-point functions. This happens both for light scalars (m < d 2 H), corresponding to complementary series representations, and heavy scalars (m > d 2 H), corresponding to principal series representations of the de Sitter group, where H is the Hubble scale of de Sitter. In the special case m = 0, only the β N autocorrelation contributes to the conjugate momentum two-point function in any dimensions and we gather hints that suggest α N to correspond to discrete series representations for this case at d = 3.
In five dimensional cosmological models, the convention is to include the fifth dimension in a wa... more In five dimensional cosmological models, the convention is to include the fifth dimension in a way similar to the other space dimensions. In this work we attempt to introduce the fifth dimension in a way that a time dimension would be introduced. With such an internal space, we are able to obtain accelerated expansion without introducing dark energy. We obtain a five dimensional flat, meaning both Ricci flat and conformally flat, spacetime into which all relevant four dimensional cosmologies can be locally embedded. We also argue on the choice of the cosmological frame. The choice that is simplest and most convenient in terms of dimensional analysis, amounts to a linearly expanding universe.
Non-thermal histories for the early universe have received notable attention as they are a rich s... more Non-thermal histories for the early universe have received notable attention as they are a rich source of phenomenology, while also being well motivated by top-down approaches to beyond the Standard Model physics. The early (pre-BBN) matter phase in these models leads to enhanced growth of density perturbations on sub-Hubble scales. Here we consider whether primordial black hole formation associated with the enhanced growth is in conflict with existing observations. Such constraints depend on the tilt of the primordial power spectrum, and we find that non-thermal histories are tightly constrained in the case of a significantly blue spectrum. Alternatively, if dark matter is taken to be of non-thermal origin we can restrict the primordial power spectrum on scales inaccessible to CMB and LSS observations. We establish constraints for a wide range of scalar masses (reheat temperatures) with the most stringent bounds resulting from the formation of 10 15 g black holes. These black holes would be evaporating today and are constrained by FERMI observations. We also consider whether the breakdown of the coherence of the scalar oscillations on sub-horizon scales can lead to a Jean's pressure preventing black hole formation and relaxing our constraints. Our main conclusion is that primordial black hole constraints, combined with existing constraints on non-thermal WIMPs, favor a primordial spectrum closer to scale invariance or a red tilted spectrum.
The Effective Field Theory (EFT) of Preheating with scalar fields, implies three types of derivat... more The Effective Field Theory (EFT) of Preheating with scalar fields, implies three types of derivative couplings between the inflaton and the reheating field. Two of these couplings lead to scales below which only one of the two species appear as the low energy modes. In this paper, the variety of low energy regimes in terms of the species they accommodate are explored by studying the scales introduced by the derivative couplings and the dispersion relations they lead to. It is noted that the EFT of two scalar fields can give rise to non-trivial sound speed for both the inflation and reheating sector even at scales where modes of both species propagate freely, suggesting the presence of additional heavy fields. The regimes where one of the species affects the dispersion relation of the other while not appearing as an effective mode itself, are named as "Hidden Regimes" during preheating.
Journal of Cosmology and Astroparticle Physics, May 23, 2016
The effective field theory of cosmic acceleration systematizes possible contributions to the acti... more The effective field theory of cosmic acceleration systematizes possible contributions to the action, accounting for both dark energy and modifications of gravity. Rather than making model dependent assumptions, it includes all terms, subject to the required symmetries, with four (seven) functions of time for the coefficients. These correspond respectively to the Horndeski and general beyond Horndeski class of theories. We address the question of whether this general systematization is actually effective, i.e. useful in revealing the nature of cosmic acceleration when compared with cosmological data. The answer is no and yes: there is no simple time dependence of the free functions -assumed forms in the literature are poor fits, but one can derive some general characteristics in early and late time limits. For example, we prove that the gravitational slip must restore to general relativity in the de Sitter limit of Horndeski theories, and why it doesn't more generally. We also clarify the relation between the tensor and scalar sectors, and its important relation to observations; in a real sense the expansion history H(z) or dark energy equation of state w(z) is 1/5 or less of the functional information! In addition we discuss the de Sitter, Horndeski, and decoupling limits of the theory utilizing Goldstone techniques.
The de Sitter spacetime is a maximally symmetric spacetime. It is one of the vacuum solutions to ... more The de Sitter spacetime is a maximally symmetric spacetime. It is one of the vacuum solutions to Einstein equations with a cosmological constant. It is the solution with a positive cosmological constant and describes a universe undergoing accelerated expansion. Among the possible signs for a cosmological constant, this solution is relevant for primordial and late-time cosmology. In the case of zero cosmological constant, studies on the representations of its isometry group have led to a broader understanding of particle physics. The isometry group of d + 1-dimensional de Sitter is the group SO(d + 1, 1), whose representations are well known. Given this insight what can we learn about the elementary degrees of freedom in a four dimensional de Sitter universe by exploring how the unitary irreducible representations of SO(4, 1) present themselves in cosmological setups? This article aims to summarize recent advances along this line that benefit towards a broader understanding of quantum field theory and holography at different signs of the cosmological constant. Particular focus is given to the manifestation of SO(4, 1) representations at the late-time boundary of de Sitter. The discussion is concluded by pointing towards future questions at the late-time boundary and the static patch with a focus on the representations.
on suitable coordinate choices and making sure that this gauge fixing, which is unavoidable in an... more on suitable coordinate choices and making sure that this gauge fixing, which is unavoidable in any calculation, does not effect the end result, is tricky. In this thesis we make full use of the effects of diffeomorphism invariance of the theory on the primordial fluctuations to pursue two different approaches that focus on treating perturbations after gauge fixing. On one hand we work towards developing our understanding of how to handle quantization in terms of Dirac quantization and Becchi, Rouet, Stora, Tyutin (BRST) quantization. On another, we focus on how to generalize the allowed interactions and understand the scales they bring in the era of preheating that follows inflation, with effective field theory (EFT) methods on cosmological backgrounds.
In five dimensional cosmological models, the convention is to include the fifth dimension in a wa... more In five dimensional cosmological models, the convention is to include the fifth dimension in a way similar to the other space dimensions. In this work we attempt to introduce the fifth dimension in a way that a time dimension would be introduced. With such an internal space, we are able to obtain accelerated expansion without introducing dark energy. Moreover our work shows that all relevant cosmologies in four dimensions can be embedded in a flat cosmology in five dimensions.
We investigate whether Effective Field Theory (EFT) approaches, which have been useful in examini... more We investigate whether Effective Field Theory (EFT) approaches, which have been useful in examining inflation and dark energy, can also be used to establish a systematic approach to inflationary reheating. We consider two methods. First, we extend Weinberg's background EFT to the end of inflation and reheating. We establish when parametric resonance and decay of the inflaton occurs, but also find intrinsic theoretical limitations, which make it difficult to capture some reheating models. This motivates us to next consider Cheung, et. al.'s EFT approach, which instead focuses on perturbations and the symmetry breaking induced by the cosmological background. Adapting the latter approach to reheating implies some new and important differences compared to the EFT of Inflation. In particular, there are new hierarchical scales, and we must account for inflaton oscillations during reheating, which lead to discrete symmetry breaking. Guided by the fundamental symmetries, we construct the EFT of reheating, and as an example of its usefulness we establish a new class of reheating models and the corresponding predictions for gravity wave observations. In this paper we primarily focus on the first stages of preheating. We conclude by discussing challenges for the approach and future directions. This paper builds on ideas first proposed in the note .
The symmetry group of the de Sitter spacetime, accommodates fields of various masses and spin amo... more The symmetry group of the de Sitter spacetime, accommodates fields of various masses and spin among its unitary irreducible representations. These unitary representations are labeled by the spin and the weight contribution to the scaling dimension and depending on the mass and spin of the field the weight may take either purely real or purely imaginary values. In this work, we construct the late time boundary operators for a massive scalar field propagating in de Sitter spacetime, in arbitrary dimensions. We show that contrary to the case of Anti de Sitter, purely imaginery weights also correspond to unitary operators, as well as the ones with real weight, and identify the corresponding unitary representations. We demonstrate that these operators correspond to the late time boundary operators and elucidate that all of them have positive definite norm.
Proceedings of Corfu Summer Institute 2021 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2021)
Our main goal here is to provide an introduction on some of the well established properties of th... more Our main goal here is to provide an introduction on some of the well established properties of the representation theory of 𝑆𝑂 (𝑑 + 1, 1), for those considering to think on physical problems set in de Sitter space in terms of these representations. With this purpose we review two intertwining maps, the map 𝐺 that is used in constructing a well defined inner product for the complementary series representations and the map 𝑄 that is involved in constructing composite representations. We give explicit examples from the late-time boundary of de Sitter on the practical use of the complementary series inner product and in building a tensor product representation from unitary principal series irreducible representations.
The de Sitter spacetime is a maximally symmetric spacetime. It is one of the vacuum solutions to ... more The de Sitter spacetime is a maximally symmetric spacetime. It is one of the vacuum solutions to Einstein equations with a cosmological constant. It is the solution with a positive cosmological constant and describes a universe undergoing accelerated expansion. Among the possible signs for a cosmological constant, this solution is relevant for primordial and late-time cosmology. In the case of a zero cosmological constant, studies on the representations of its isometry group have led to a broader understanding of particle physics. The isometry group of d+1-dimensional de Sitter is the group SO(d+1,1), whose representations are well known. Given this insight, what can we learn about the elementary degrees of freedom in a four dimensional de Sitter universe by exploring how the unitary irreducible representations of SO(4,1) present themselves in cosmological setups? This article aims to summarize recent advances along this line that benefit towards a broader understanding of quantum f...
We demonstrate how free massive scalar fields in the set up that usually appears in early univers... more We demonstrate how free massive scalar fields in the set up that usually appears in early universe inflationary studies, correspond to the principal series and complementary series representations of the group SO(d+1,1) by introducing late-time operators and computing their two-point functions.
The Effective Field Theory (EFT) of Preheating with scalar fields, implies three types of derivat... more The Effective Field Theory (EFT) of Preheating with scalar fields, implies three types of derivative couplings between the inflaton and the reheating field. Two of these couplings lead to scales below which only one of the two species appear as the low energy modes. In this paper, the possibility of low energy regimes in terms of the species they accommodate are explored by studying the scales introduced by the derivative couplings and the dispersion relations they lead to. It is noted that the EFT of two scalar fields can give rise to non-trivial sound speed for both the inflation and reheating sector even at scales where modes of both species propagate freely, suggesting the presence of additional heavy fields. The regimes where one of the species affects the dispersion relation of the other while not appearing as an effective mode itself, are named as "Hidden Regimes" during preheating.
In this note we propose a model independent framework for inflationary (p)reheating. Our approach... more In this note we propose a model independent framework for inflationary (p)reheating. Our approach is analogous to the Effective Field Theory of Inflation, however here the inflaton oscillations provide an additional source of (discrete) symmetry breaking. Using the Goldstone field that nonlinearly realizes time diffeormorphism invariance we construct a model independent action for both the inflaton and reheating sectors. Utilizing the hierarchy of scales present during the reheating process we are able to recover known results in the literature in a simpler fashion, including the presence of oscillations in the primordial power spectrum. We also construct a class of models where the shift symmetry of the inflaton is preserved during reheating, which helps alleviate past criticisms of (p)reheating in models of Natural Inflation. Extensions of our framework suggest the possibility of analytically investigating non-linear effects (such as rescattering and back-reaction) during thermali...
The symmetry group of the de Sitter spacetime, accommodates fields of various masses and spin amo... more The symmetry group of the de Sitter spacetime, accommodates fields of various masses and spin among its unitary irreducible representations. These unitary representations are labeled by the spin and the weight contribution to the scaling dimension and depending on the mass and spin of the field the weight may take either purely real or purely imaginary values. In this work, we construct the late time boundary operators for a massive scalar field propagating in de Sitter spacetime, in arbitrary dimensions. We show that contrary to the case of Anti de Sitter, purely imaginery weights also correspond to unitary operators, as well as the ones with real weight, and identify the corresponding unitary representations. We demonstrate that these operators correspond to the late time boundary operators and elucidate that all of them have positive definite norm.
The Effective Field Theory (EFT) of Preheating with scalar fields, implies three types of derivat... more The Effective Field Theory (EFT) of Preheating with scalar fields, implies three types of derivative couplings between the inflaton and the reheating field. Two of these couplings lead to scales below which only one of the two species appear as the low energy modes. In this paper, the variety of low energy regimes in terms of the species they accommodate are explored by studying the scales introduced by the derivative couplings and the dispersion relations they lead to. It is noted that the EFT of two scalar fields can give rise to non-trivial sound speed for both the inflation and reheating sector even at scales where modes of both species propagate freely, suggesting the presence of additional heavy fields. The regimes where one of the species affects the dispersion relation of the other while not appearing as an effective mode itself, are named as "Hidden Regimes" during preheating.
We investigate whether Effective Field Theory (EFT) approaches, which have been useful in examini... more We investigate whether Effective Field Theory (EFT) approaches, which have been useful in examining inflation and dark energy, can also be used to establish a systematic approach to inflationary reheating. We consider two methods. First, we extend Weinberg's background EFT to the end of inflation and reheating. We establish when parametric resonance and decay of the inflaton occurs, but also find intrinsic theoretical limitations, which make it difficult to capture some reheating models. This motivates us to next consider Cheung, et. al.'s EFT approach, which instead focuses on perturbations and the symmetry breaking induced by the cosmological background. Adapting the latter approach to reheating implies some new and important differences compared to the EFT of Inflation. In particular, there are new hierarchical scales, and we must account for inflaton oscillations during reheating, which lead to discrete symmetry breaking. Guided by the fundamental symmetries, we construct the EFT of reheating, and as an example of its usefulness we establish a new class of reheating models and the corresponding predictions for gravity wave observations. In this paper we primarily focus on the first stages of preheating. We conclude by discussing challenges for the approach and future directions. This paper builds on ideas first proposed in the note .
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Papers by Gizem Sengor