Chain inflation is an alternative to slow-roll inflation in which the inflaton tunnels along a large number of consecutive minima in its potential. In this work we perform the first comprehensive calculation of the gravitational wave (GW) spectrum of chain inflation. In contrast to slow-roll inflation the latter does not stem from quantum fluctuations of the gravitational field during inflation, but rather from the bubble collisions during the first-order phase transitions associated with vacuum tunneling. Our calculation is performed within an effective theory of chain inflation which builds on an expansion of the tunneling rate capturing most of the available model space. The effective theory can be seen as chain inflation’s analog of the slow-roll expansion in rolling models of inflation. The near scale-invariance of the scalar power spectrum translates to a quasiperiodic shape of the inflaton potential in chain inflation, with the tunneling rate changing very slowly during the e-folds leading to cosmic microwave background observables. We show that chain inflation produces a very characteristic double-peak GW spectrum: a faint high-frequency peak associated with the gravitational radiation emitted during inflation, and a strong low-frequency peak associated with the graceful exit from chain inflation (marking the transition to the radiation-dominated epoch). There exist very exciting prospects to test the gravitational wave signal from chain inflation at the aLIGO-aVIRGO-KAGRA network, at LISA and /or at pulsar timing array experiments. A particularly intriguing possibility we point out is that chain inflation could be the source of the stochastic gravitational wave background recently detected by NANOGrav, PPTA, EPTA, and CPTA. We also show that the gravitational wave signal of chain inflation is often accompanied by running/ higher running of the scalar spectral index to be tested at future cosmic microwave background experiments.

The paradigm of inflation –  a period of accelerated expansion in the very early Universe –  was introduced to give solutions to a number of problems encountered in Standard Big Bang cosmology. Additionally, due to its quantum nature, inflation is able to generate the necessary primordial inhomogeneity “seeds”, which eventually evolve into large-scale structures. The particular primordial inhomogeneities are imprinted on the Cosmic Microwave Background radiation (CMB) as very small deviations –  temperature fluctuations –  from a perfect blackbody spectrum. If the Standard Model (SM) Higgs is a light spectator field during inflation, it can acquire quantum fluctuations and seed additional, potentially observable, fluctuations. This takes place via an effective breaking of electroweak symmetry at very high energy scales, which results in the reheating process being different in different regions of the Universe. In the first part of the research work, we develop methods for calculating the amplitude, as well as the non-Gaussianity, of such Higgs-induced temperature fluctuations in the CMB. In the case of reheating via resonant inflaton decays to Abelian gauge bosons, we show that the amplitude of the Higgs-induced temperature fluctuations always exceeds the observed value and that, therefore, such decays cannot be the main reheating channel. In the case of reheating via perturbative inflaton decays to SM fermions, we place strong constraints on the relevant SM parameters, using the amplitude of the Higgs temperature fluctuations. By additionally using the associated non-Gaussianity, we are able to strengthen the particular constraints even further. Having made a connection between cosmological observations and SM parameters, such as the Higgs self-coupling, we suggest a way to probe the SM Higgs potential at very high energy scales and constrain New Physics. In the second part of the research work we study a specific inflationary model, known as chain inflation. In particular, we calculate the primordial gravitational wave (GW) signatures produced by chain inflation. We show that the latter can explain the GW stochastic background detected by the International Pulsar Timing Array (IPTA). Finally, we show that GW signatures of chain inflation are detectable both by current and/or by future GW instruments.

The cosmological constant and its phenomenology remain among the greatest puzzles in theoretical physics. We review how modifications of Einstein’s general relativity could alleviate the different problems associated with it that result from the interplay of classical gravity and quantum field theory. We introduce a modern and concise language to describe the problems associated with its phenomenology, and inspect no-go theorems and their loopholes to motivate the approaches discussed here. Constrained gravity approaches exploit minimal departures from general relativity; massive gravity introduces mass to the graviton; Horndeski theories lead to the breaking of translational invariance of the vacuum; and models with extra dimensions change the symmetries of the vacuum. We also review screening mechanisms that have to be present in some of these theories if they aim to recover the success of general relativity on small scales as well. Finally, we summarize the statuses of these models in their attempts to solve the different cosmological constant problems while being able to account for current astrophysical and cosmological observations.

We propose a new way of studying the Higgs potential at extremely high energies. The Standard Model (SM) Higgs boson, as a light spectator field during inflation in the early Universe, can acquire large field values from its quantum fluctuations which vary among different causal (Hubble) patches. Such a space dependence of the Higgs after the end of inflation leads to space-dependent SM particle masses and hence variable efficiency of reheating, when the inflaton decays to Higgsed SM particles. Inhomogeneous reheating results in (observable) temperature anisotropies. Further, the resulting temperature anisotropy spectrum acquires a significant non-Gaussian component, which is constrained by Planck observations of the Cosmic Microwave Background (CMB) and potentially detectable in next-generation experiments. Constraints on this non-Gaussian signal largely exclude the possibility of the observed temperature anisotropies arising primarily from Higgs effects. Hence, in principle, observational searches for non-Gaussianity in the CMB can be used to constrain the dynamics of the Higgs boson at very high (inflationary) energies.

The model of inflation - a period of accelerated expansion in the very early Universe - was introduced to give solutions to a number of problems encountered in the Standard Big Bang paradigm. Additionally, due to its quantum nature, inflation is able to generate the necessary primordial inhomogeneity “seeds”, which eventually evolve into large-scale structures. The particular primordial inhomogeneities are imprinted on the Cosmic Microwave Background radiation (CMB) as very small deviations (temperature fluctuations) from a perfect blackbody spectrum. If the Standard Model (SM) Higgs is a light spectator field during inflation, it can, also, acquire quantum fluctuations and seed additional, potentially observable, fluctuations. This takes place via an effective breaking of electroweak symmetry at very high energy scales, which results in the reheating process being different in different regions of the Universe. We develop methods for calculating the amplitude, as well as the non-Gaussianity, of such Higgs-induced temperature fluctuations in the CMB. In the case of reheating via resonant inflaton decays to Abelian gauge bosons, we show that the amplitude of the Higgs-induced temperature fluctuations always exceeds the observed value and that, therefore, such decays cannot be the main reheating channel. In the case of reheating via perturbative inflaton decays to SM fermions, we place strong constraints on the relevant SM parameters, using the amplitude of the Higgs temperature fluctuations. By additionally using the associated non-Gaussianity, we are able to strengthen the particular constraints even further. Having made a connection between cosmological observations and SM parameters, such as the Higgs self-coupling, we suggest a way to probe the SM Higgs potential at very high energy scales and constrain New Physics.

In Chain Inflation the universe tunnels along a series of false vacua of ever-decreasing energy. The main goal of this paper is to embed Chain Inflation in high energy fundamental physics. We begin by illustrating a simple effective formalism for calculating Cosmic Microwave Background (CMB) observables in Chain Inflation. Density perturbations seeding the anisotropies emerge from the probabilistic nature of tunneling (rather than from quantum fluctuations of the inflation). To obtain the correct normalization of the scalar power spectrum and the scalar spectral index, we find an upper limit on the scale of inflation at horizon crossing of CMB scales, V_∗^1/4<10¹² GeV. We then provide an explicit realization of chain inflation, in which the inflaton is identified with an axion in supergravity. The axion enjoys a perturbative shift symmetry which is broken to a discrete remnant by instantons. The model, which we dub ‘natural chain inflation’ satisfies all cosmological constraints and can be embedded into a standard ΛCDM cosmology. Our work provides a major step towards the ultraviolet completion of chain inflation in string theory.

Cosmic microwave background observations are used to constrain reheating to standard model (SM) particles after a period of inflation. As a light spectator field, the SM Higgs boson acquires large field values from its quantum fluctuations during inflation, gives masses to SM particles that vary from one Hubble patch to another, and thereby produces large density fluctuations. We consider both perturbative and resonant decay of the inflaton to SM particles. For the case of perturbative decay from coherent oscillations of the inflaton after high scale inflation, we find strong upper bounds on the reheat temperature for the inflaton decay into heavy SM particles. The strongest bounds arise in the case of reheating to top quarks where we find Treh less than or similar to Oo1012 thorn GeV for an inflaton mass of 1013 GeV. For the case of resonant particle production (preheating) to (Higgsed) SM gauge bosons, we find temperature fluctuations larger than observed in the cosmic microwave background for a range of gauge coupling that includes those found in the SM and conclude that such preheating cannot be the main source of reheating the Universe after inflation.

We propose a new way of studying the Higgs potential at extremely high energies. The SM Higgs boson, as a light spectator field during inflation in the early Universe, can acquire large field values from its quantum fluctuations which vary among different causal (Hubble) patches. Such a space dependence of the Higgs after the end of inflation leads to space-dependent SM particle masses and hence variable efficiency of reheating, when the inflaton decays to Higgsed SM particles. Inhomogeneous reheating results in (observable) temperature anisotropies. Further, the resulting temperature anisotropy spectrum acquires a significant non-Gaussian component, which is constrained by Planck observations of the Cosmic Microwave Background (CMB) and potentially detectable in next-generation experiments. Constraints on this non-Gaussian signal largely exlcude the possibility of the observed temperature anisotropies arising primarily from Higgs effects. Hence, in principle, observational searches for non-Gaussianity in the CMB can be used to constrain the dynamics of the Higgs boson at very high (inflationary) energies.