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Local measurements of the Hubble parameter obtained from the distance ladder at low redshift are in tension with global values inferred from cosmological standard rulers. A key role in the tension is played by the assumptions on the cosmological history, in particular on the origin of dark energy. Here we consider a scenario where dark energy originates from the amplification of quantum fluctuations of a light field in inflation. We show that spatial correlations inherited from inflationary quantum fluctuations can reduce the Hubble tension down to one standard deviation, thus relieving the problem with respect to the standard cosmological model. Upcoming missions, like Euclid, will be able to test the predictions of models in this class., Comment: v2: version published in Phys. Lett. B; added references, added appendix on evolution of 4-pt functions; 20 pages, 2 figures

We consider single graviton loop corrections to the effective field equation of a massless, minimally coupled scalar on de Sitter background in the simplest gauge. We find a large temporal logarithm in the approach to freeze-in at late times, but no correction to the feeze-in amplitude. We also find a large spatial logarithm (at large distances) in the scalar potential generated by a point source, which can be explained using the renormalization group with one of the higher derivative counterterms regarded as a curvature-dependent field strength renormalization. We discuss how these results set the stage for a project to purge gauge dependence by including quantum gravitational corrections to the source which disturbs the effective field and to the observer who measures it., Comment: 26 pages, 2 figures, uses LaTeX2e, Version 2 revised slightly for publication

Conjugate points play an important role in the proofs of the singularity theorems of Hawking and Penrose. We examine the relation between singularities and conjugate points in FLRW spacetimes with a singularity. In particular we prove a theorem that when a non-comoving, non-spacelike geodesic in a singular FLRW spacetime obeys conditions (39) and (40), every point on that geodesic is part of a pair of conjugate points. The proof is based on the Raychaudhuri equation. We find that the theorem is applicable to all non-comoving, non-spacelike geodesics in FLRW spacetimes with non-negative spatial curvature and scale factors that near the singularity have power law behavior or power law behavior times a logarithm. When the spatial curvature is negative, the theorem is applicable to a subset of these spacetimes.

Ultraviolet completion of the standard model plus gravity at and beyond the Planck scale is a daunting problem to which no generally accepted solution exists. Principal obstacles include (a) lack of data at the Planck scale (b) nonrenormalizability of gravity and (c) unitarity problem. Here we make a simple observation that, if one treats all Planck scale operators of equal canonical dimension democratically, one can tame some of the undesirable features of these models. With a reasonable amount of fine tuning one can satisfy slow roll conditions required in viable inflationary models. That remains true even when the number of such operators becomes very large., Comment: 9 pages, 0 figures

We propose gravitational microlensing as a way of testing the emergent gravity theory recently proposed by Eric Verlinde [1]. We consider two limiting cases: the dark mass of maximally anisotropic pressures (Case I) and of isotropic pressures (Case II). Our analysis of perihelion advancement of a planet shows that only Case I yields a viable theory. In this case the metric outside a star of mass M⁎ can be modeled by that of a point-like global monopole whose mass is M⁎ and a deficit angle Δ=(2GH0M⁎)/(3c3), where H0 is the Hubble rate and G the Newton constant. This deficit angle can be used to test the theory since light exhibits additional bending around stars given by, αD≈−πΔ/2. This angle is independent on the distance from the star and it affects equally light and massive particles. The effect is too small to be measurable today, but should be within reach of the next generation of high resolution telescopes. Finally we note that the advancement of periastron of a planet orbiting around a star or black hole, which equals πΔ per period, can be also used to test the theory.

We investigate the backreaction of the quantum fluctuations of a very light ($m \!\lesssim\! H_{\text{today}}$) nonminimally coupled spectator scalar field on the expansion dynamics of the Universe. The one-loop expectation value of the energy momentum tensor of these fluctuations, as a measure of the backreaction, is computed throughout the expansion history from the early inflationary universe until the onset of recent acceleration today. We show that, when the nonminimal coupling $\xi$ to Ricci curvature is negative ($\xi_c \!=\! 1/6$ corresponding to conformal coupling), the quantum backreaction grows exponentially during inflation, such that it can grow large enough rather quickly (within a few hundred e-foldings) to survive until late time and constitute a contribution of the cosmological constant type of the right magnitude to appreciably alter the expansion dynamics. The unique feature of this model is in that, under rather generic assumptions, inflation provides natural explanation for the initial conditions needed to explain the late-time accelerated expansion of the Universe, making it a particularly attractive model of dark energy., Comment: 66 pages, 6 figures

We point out that past-incompleteness of geodesics in FLRW spacetimes does not necessarily imply that these spacetimes start from a singularity. Namely, if a test particle that follows such a trajectory has a non-vanishing velocity, its energy was super-Planckian at some time in the past if it kept following that geodesic. That indicates a breakdown of the particle's description, which is why we should not consider those trajectories for the definition of an initial singularity. When one only considers test particles that do not have this breakdown of their trajectory, it turns out that the only singular FLRW spacetimes are the ones that have a scale parameter that vanishes at some initial time. Keywords: FLRW spacetime, Incomplete geodesics, Singularity

We evaluate the one-graviton loop contribution to the vacuum polarization on de Sitter background in a 1-parameter family of exact, de Sitter invariant gauges. Our result is computed using dimensional regularization and fully renormalized with BPHZ counterterms, which must include a noninvariant owing to the time-ordered interactions. Because the graviton propagator engenders a physical breaking of de Sitter invariance two structure functions are needed to express the result. In addition to its relevance for the gauge issue this is the first time a covariant gauge graviton propagator has been used to compute a noncoincident loop. A number of identities are derived which should facilitate further graviton loop computations., Comment: 61 pages, 1 figure, 11 tables, version 2 (63 pages) revised for publication in CQG

We consider inflation in a universe with a positive cosmological constant and a nonminimally coupled scalar field, in which the field couples both quadratically and quartically to the Ricci scalar. When considered in the Einstein frame and when the nonminimal couplings are negative, the field starts in slow roll and inflation ends with an asymptotic value of the principal slow roll parameter, $\epsilon_E=4/3$. Graceful exit can be achieved by suitably (tightly) coupling the scalar field to matter, such that at late time the total energy density reaches the scaling of matter, $\epsilon_E=\epsilon_m$. Quite generically the model produces a red spectrum of scalar cosmological perturbations and a small amount of gravitational radiation. With a suitable choice of the nonminimal couplings, the spectral slope can be as large as $n_s\simeq 0.955$, which is about one standard deviation away from the central value measured by the Planck satellite. The model can be ruled out by future measurements if any of the following is observed: (a) the spectral index of scalar perturbations is $n_s>0.960$; (b) the amplitude of tensor perturbations is above about $r\sim 10^{-2}$; (c) the running of the spectral index of scalar perturbations is positive., Comment: 19 pages, 13 figures

Large-scale structure formation is arguably one of the most important problems of modern cosmology. The standard treatment is based on a point-particle picture and the corresponding Vlasov equation. Here, we take a field-theoretic approach to this problem and identify how field correlators in curved-space time are related to classical particle distributions in phase-space. We obtain the Vlasov equation in a well-defined limit together with field-theoretic corrections which can be studied in a controlled way. We also take a fresh look at the initial conditions for the cosmic microwave background and large-scale structure formation by presenting a two-field inflationary model in which the inflaton couples bi-quadratically to a light spectator field. The spectator induces a rapid production of entropy which significantly alters the initial conditions for the cosmological evolution at the end of inflation by providing large, stochastically independent momentum fluctuations of the gauge invariant curvature perturbation.

In this thesis we study both classical and quantum properties of a gauge realisation of Weyl symmetry, achieved by endowing the space-time manifold with a torsional connection. Some component of torsion can then act as a gauge connection, thus compensating the local transformations of the metric tensor and the fields. This leads to a rather generic physical theory, described in chapter 2, which features a dilaton and a vector field on top of the usual particle content of the standard model. We then study a possible mechanism that spontaneous breaks conformal symmetry, showing that cosmological inflation can be described in such a framework. The resulting model has notable features and agrees with inflationary observables in a wide range of the parameter space. In chapter 4 we discuss detection of torsion by means of gravitational waves detectors, which is within range of experimental approach once the space based gravitational detectors will be online. Finally in chapter 5 we address the conformal anomaly and present first evidence that the extended Ward identity, which take into account the additional vector field, hold in a perturbative dimensional renormalization scheme, even when anomalous contributions are generated in the energy momentum tensor trace.

This thesis explores two windows into fundamental physics: (1) textbf{Cosmic inflation}: By considering inflation as a window to the physics at high energies and to quantum gravity, we study two inflationary models. In one model, we study the quantum corrections for Starobinsky's inflationary model cite{Starobinsky:1980te}, in which we investigate how are cosmological observables affected by quantum effects. Our results show that these observables are significantly affected, but they still agree with observations. We stress that the significant deviations from Starobinsky's inflationary model can be used to study and constrain the quantum loop effects during inflation. The other model is a curvaton model, in which the quantum effects induce a non-minimal coupling to gravity. We find that the non-minimal coupling could use to tune the scalar power spectral index $n_s$ and the power spectrum $P_zeta$. (2) textbf{Emergent gravity}: Statistical laws of black hole suggest that gravity is not fundamental but instead of an emergent phenomenon. One such theory was proposed by Verlinde~cite{Verlinde:2016toy}. In order to test the validity of his theory, we propose two tests of the theory: the perihelion advancement of a planet and the microlensing. We find that Verlinde's theory can be probed by the next generation of experiments.

In this thesis the mathematical formulation of cosmological perturbations is studied. First we discuss the gauge problem of general relativity: perturbations of the metric and matter fields in an expanding universe are dependent on the choice of coordinate system, i.e. gauge dependent, even though the complete, unperturbed theory is covariant. Secondly, we discuss the frame problem of perturbations: the action for a universe with scalar field matter can be formulated in two different ways, in the Jordan or Einstein frame. These formulations are related by redefinitions of the metric and scalar field, and are therefore physically equivalent. However, perturbations in one frame and another are related by non-linear redefinitions, which makes it complicated to see how to formulate physical correlation functions. In this thesis we show that it is possible to express the action for perturbations in terms of gauge invariant and frame independent perturbations. These perturbations are then used to compute physical correlation functions which are independent of coordinate reparametrizations or field redefinitions. We first compute the second order action for linear perturbations. Later we outline a procedure to compute the action for non-linear perturbations, and apply this to find the gauge invariant action for second order perturbations. We furthermore show that there are different gauge invariant variables related by non-linear redefinitions, but that their actions are only related by boundary terms, such that the evolution of non-Gaussianity is unique. Moreover, as a final application we use the formulation of the action in terms of gauge invariant and frame independent variables in order to readdress the naturalness in Higgs inflation. In this formulation, Higgs inflation does not suffer from unitarity problems.

Quantum field theory is indispensable for understanding many aspects of cosmology, both in the early Universe and today. For example, quantum processes could be paramount to understand the nature of the mysterious dark energy resulting in the Universe’s recently observed accelerated expansion. Inspired by these considerations, this PhD thesis is concerned with two aspects of quantum field theory relevant to cosmology: quantum backreaction and decoherence. Quantum backreaction is a line of research where the impact of quantum fluctuations on the background spacetime geometry in perturbative quantum gravity is investigated. The cosmological constant problem and the process of quantum backreaction are intimately related: quantum backreaction might provide us with a dynamical mechanism to effectively make the cosmological constant almost vanish. We investigate the quantum backreaction of the trace anomaly and of fermions. We find that the trace anomaly does not dynamically influence the effective value of the cosmological constant. We furthermore evaluate the fermion propagator in FLRW spacetimes with constant deceleration. Although the dynamics resulting from the one-loop stress-energy tensor need yet to be investigated, we find that we certainly cannot exclude a significant effect due to the quantum backreaction on the Universe’s expansion. Decoherence is a quantum theory which addresses the quantum-to-classical transition of a particular system. The idea of the decoherence formalism is that a macroscopic system cannot be separated from its environment. The framework of decoherence is widely used, e.g. in quantum computing, black hole physics, inflationary perturbation theory, and in elementary particle physics, such as electroweak baryogenesis models. We formulate a novel “correlator approach” to decoherence: neglecting observationally inaccessible correlators gives rise to an increase in entropy of the system, as perceived by an observer. This is inspired by realising that higher order, non-Gaussian correlators are usually perturbatively suppressed. A quantum system with a large entropy corresponds to an effectively classical, stochastic system. To allow for a quantitative comparison between our correlator approach and the conventional approach to decoherence, we apply both formalisms to two simple quantum mechanical models. We find that the entropy in the conventional approach to decoherence quite generically reveals secular growth, indicating physically unacceptable behaviour. The conventional approach furthermore suffers from the fact that no well-established treatment to take perturbative corrections into account exists, nor has the framework of renormalisation ever been implemented. Our correlator approach to decoherence is taylored to applications in quantum field theory. We perform the first realistic study of decoherence in a renormalised quantum field theoretical setting. Using out-of-equilibrium field theory techniques, we extract two quantitative measures of decoherence in our model: the total amount of decoherence and the decoherence rate. The main finding in this part of the thesis is that, although a pure state remains pure under unitary evolution, an observer perceives this state over time as a mixed state with positive entropy as non-Gaussianities are dynamically generated. Alternatively, one could say that a realistic observer cannot probe all information about the system and thus discerns a loss of coherence of the pure state

In this thesis the infrared properties of massless scalar fields, with a possible coupling to the Ricci scalar on a cosmological background are studied. Our background space-time is a homogeneous, flat FLRW space-time, with the additional constraint that the deceleration parameter is constant. It has been known for a long time that the propagator of such a scalar field diverges at the lower end of the integration over the momenta when evaluated for the Bunch-Davies vacuum. The resolution we propose to this problem is to work on a spatially compact universe. This effectively generates an infrared cut-off in the integral over the mode functions. To see what the physical effect of this approaches is, we calculated the expectation value of the stress energy tensor. Using the infrared regulated propagator, we find in the ultraviolet that we correctly reproduce the Bunch-Davies result. In the infrared the discussion can be split in two parts. If the universe is accelerating we found that, although we see a growth in energy due to the production of infrared particles, this energy will always dilute away faster than the energy present in the background space-time. In a decelerating universe the situation is quite different. We find that, since in a decelerating universe, the Hubble radius grows faster then physical scales, the cut-off scale actually enters the Hubble volume. This results in a large effect which is thus not due to particle creation, but it is due to the fact that the influence of the cut-off grows more and more profound as time goes on. We also calculated the one loop effective action in a theory where both gravity and a scalar field produce quantum fluctuations. The mixing between the dynamical degrees of freedom in such a case leads to more complicated expressions, but in the end the final answer is very similar to the obtained expectation value of the stress energy tensor for just a single massless scalar field. Also for the graviton we find that at one loop order all growth in energy due to the creation of infrared modes is cancelled by the redshift of these modes. As a second application we used the cut-off regulated propagator to calculate the one-loop effective potential for a massless scalar field, with a coupling to the Ricci scalar and a quartic self interaction. We calculated the effective action by assuming that the background field has the same time dependence as the Hubble parameter. While this is true at the classical level, this scaling turns out to be broken by the quantum corrections. Furthermore we find that initially, the quantum corrections can induce a phase transition, by generating minima in the potential for nonzero field values. However the growing infrared contributions are such that, after a sufficient amount of time, the effective potential will always end up with only one minimum at the origin. Thus the infrared modes have restored the symmetry of the potential.