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.

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.

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 [1].

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.

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.