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A bstract We give an explicit example of a composite Higgs model with a pseudo-Nambu-Goldstone Higgs in which the top Yukawa coupling is generated via the partial compositeness mechanism. This mechanism requires composite top partners which are relatively light compared to the typical mass scale of the strongly coupled theory. While most studies of the phenomenology of such models have focused on a bottom-up approach with a minimal effective theory, a top-down approach suggests that the theory should contain a limit in which an unbroken global chiral symmetry protects the mass of the top partners, and the spectrum of the partners satisfies ‘t Hooft matching conditions. We find that the relatively light fermions and pseudo-Goldstone bosons fall into complete multiplets of a large approximate global symmetry, and that the spectrum of particles lighter than a few TeV is non-minimal. Our example illustrates the likely features of a such a composite Higgs theory and also serves as an example of a non-chiral theory with a possible solution to the ‘t Hooft matching conditions. We find in this example that for some low-energy parameters in the effective theory the top partners can decay into high-multiplicity final states, which could be difficult for the Large Hadron Collider (LHC) to constrain. This may potentially allow for the top partners to be lighter than those in more minimal models.

A bstract We make an extension to recent calculations of the probability density ρ ( V ) for the volume of the universe after inflation. Previous results have been accurate to leading order in the slow roll parameters ∈ ≡ H ⋅ / H 2 and η ≡ ϕ ⋅⋅ / ϕ ⋅ H , and 1 /N c , where H is the Hubble parameter and N c is the classical number of e -foldings. Here, we present a modification which captures effects of order ϵN c , which amounts to letting the parameters of inflation H and ϕ ⋅ depend on the value of the inflaton ϕ . The phase of slow roll eternal inflation can be defined as when the probability to have an infinite volume is greater than zero. Using this definition, we study the Laplace transform of ρ ( V ) numerically to determine the condition that triggers the transition to eternal inflation. We also study the average volume 〈 V 〉 analytically and show that it satisfies the universal volume bound. This bound states that, in any realization of inflation which ends with a finite volume, an initial volume must grow by less than a factor of e S d S / 2 , where S dS is the de Sitter (dS) entropy.

Effective field theory (EFT) is our most successful tool to date for exploring the fundamental processes of particle physics: it has been able to describe all know particle interactions in the lab to astonishing accuracy. We are now entering an era of precision cosmology, where we can use the power of EFT, a tool that has only recently been applied to the field of cosmology, to fully make use of cosmological observations. This thesis comprises recent work applying effective field theory in the context of early-universe cosmology and large-scale structure (LSS).Observations of the cosmic microwave background (CMB) have not yet found evidence of primordial non-gaussianity, a key signature of the interactions during inflation. However, surveys of the distribution of the large-scale structure of matter in the universe have the potential to produce limits competitive with CMB surveys because they map the universe in three dimensions, while the CMB is a two-dimensional snapshot of an instant in time. Compared to the CMB, however, this field possesses considerable hurdles in matching primordial signals to observations. While the CMB was produced at an early enough time that its structures were formed by linear evolution of the primordial signal, large-scale structure (LSS) is observed at late times, when the primordial signal has been obscured due to the non-linear clustering of gravity. The nonlinear clustering of matter is a problem well suited for EFT, because in the bottom-up approach, we can “integrate out” the small-scale dynamics of the matter, parameterizing its effect on large scales in a spatial-derivative expansion suppressed by the scale at which the density perturbation becomes nonlinear.The work of the first half of this thesis uses EFT to extends our understanding of inflation in the quasi-nonlinear regime, by extending the inflationary consistency conditions to second order, and including slow-roll corrections to the phase transition to eternal inflation. The latter part explores the use of EFT in LSS, including introducing the effects of normal (baryonic) matter to the theory, which previously described only dark matter, and making the first step from theory to observations by computing the statistics of different populations of halos and galaxies measured in redshift space.

The Effective Field Theory of Large-Scale Structure (EFTofLSS) provides a consistent perturbative framework for describing the statistical distribution of cosmological large-scale structure. In a previous EFTofLSS calculation that involved the one-loop power spectra and tree-level bispectra, it was shown that the \\(k\\)-reach of the prediction for biased tracers is comparable for all investigated masses if suitable higher-derivative biases, which are less suppressed for more massive tracers, are added. However, it is possible that the non-linear biases grow faster with tracer mass than the linear bias, implying that loop contributions could be the leading correction to the bispectra. To check this, we include the one-loop contributions in a fit to numerical data in the limit of strongly enhanced higher-order biases. We show that the resulting one-loop power spectra and higher-derivative plus leading one-loop bispectra fit the two- and three-point functions respectively up to \\(k\\simeq 0.19\\ h\\ \\rm{Mpc}^{-1}\\) and \\(k\\simeq 0.14\\ h\\ \\rm{Mpc}^{-1}\\) at the percent level. We find that the higher-order bias coefficients are not strongly enhanced, and we argue that the gain in perturbative reach due to the leading one-loop contributions to the bispectra is relatively small. Thus, we conclude that higher-derivative biases provide the leading correction to the bispectra for tracers of a very wide range of masses.

We make an extension to recent calculations of the probability density \\rho(V) for the volume of the universe after inflation. Previous results have been accurate to leading order in the slow roll parameters \\epsilon=\\dot{H}/H^2 and \\eta=\\ddot{\\phi}/(\\dot{\\phi} H), and 1/N_c, where H is the Hubble parameter and N_c is the classical number of e-foldings. Here, we present a modification which captures effects of order \\epsilon N_c, which amounts to letting the parameters of inflation H and \\dot{\\phi} depend on the value of the inflaton \\phi. The phase of slow roll eternal inflation can be defined as when the probability to have an infinite volume is greater than zero. Using this definition, we study the Laplace transform of \\rho(V) numerically to determine the condition that triggers the transition to eternal inflation. We also study the average volume analytically and show that it satisfies the universal volume bound. This bound states that, in any realization of inflation which ends with a finite volume, an initial volume must grow by less than a factor of exp(S_{dS}/2), where S_{dS} is the de Sitter (dS) entropy.

The large scale structures of the universe will likely be the next leading source of cosmological information. It is therefore crucial to understand their behavior. The Effective Field Theory of Large Scale Structures provides a consistent way to perturbatively predict the clustering of dark matter at large distances. The fact that baryons move distances comparable to dark matter allows us to infer that baryons at large distances can be described in a similar formalism: the backreaction of short-distance non-linearities and of star-formation physics at long distances can be encapsulated in an effective stress tensor, characterized by a few parameters. The functional form of baryonic effects can therefore be predicted. In the power spectrum the leading contribution goes as \\(\\propto k^2 P(k)\\), with \\(P(k)\\) being the linear power spectrum and with the numerical prefactor depending on the details of the star-formation physics. We also perform the resummation of the contribution of the long-wavelength displacements, allowing us to consistently predict the effect of the relative motion of baryons and dark matter. We compare our predictions with simulations that contain several implementations of baryonic physics, finding percent agreement up to relatively high wavenumbers such as \\(k\\simeq 0.3\\,h\\, Mpc^{-1}\\) or \\(k\\simeq 0.6\\, h\\, Mpc^{-1}\\), depending on the order of the calculation. Our results open a novel way to understand baryonic effects analytically, as well as to interface with simulations.

Models in which the dark matter is produced at extremely low rates from the annihilation of Standard Model particles in the early Universe allow us to explain the current dark matter relic density while easily evading the traditional experimental constraints. In scenarios where the dark matter interacts with the Standard Model via a new physics mediator, the early Universe dynamics of the dark sector can be particularly complex, as the dark matter and the mediator could be in thermal and chemical equilibrium with each other. This equilibration takes place via number-changing processes such as double Compton scattering and bremsstrahlung, whose amplitudes are cumbersome to calculate. In this paper, we show that in large regions of the parameter space, these equilibration mechanisms do not significantly affect the final dark matter relic density. In particular, for a model with a light dark photon mediator, the relic density can be reasonably estimated by considering that the dark matter is solely produced through the annihilation of Standard Model particles. This result considerably simplifies the treatment of a large class of dark matter theories, facilitating in particular the superimposition of the relic density constraints on the current and future experimental bounds.

We give an explicit example of a composite Higgs model with a pseudo-Nambu-Goldstone Higgs in which the top Yukawa coupling is generated via the partial compositeness mechanism. This mechanism requires composite top partners which are relatively light compared to the typical mass scale of the strongly coupled theory. While most studies of the phenomenology of such models have focused on a bottom-up approach with a minimal effective theory, a top-down approach suggests that that the theory should contain a limit in which an unbroken global chiral symmetry protects the mass of the top partners, and the spectrum of the partners satisfies `t Hooft matching conditions. We therefore consider a model for the UV gauge group which could provide a solution to the matching conditions, and note that the relatively light fermions and pseudo-Goldstone bosons fall into complete multiplets of a large approximate global symmetry. This implies that the spectrum of particles lighter than a few TeV is non-minimal. Our example illustrates likely features of a composite Higgs theory, and also serves as an example of a non-chiral theory with no sign problem and a possible solution to `t Hooft matching conditions. It would therefore be very interesting for a lattice exploration. We find in this example that for some low-energy parameters in the effective theory the top partners can decay into high multiplicity final states, which could be difficult for the Large Hadron Collider (LHC) to constrain. This may potentially allow for the top partners to be lighter than those in more minimal models.

The Effective Field Theory of Large-Scale Structure (EFTofLSS) provides a novel formalism that is able to accurately predict the clustering of large-scale structure (LSS) in the mildly non-linear regime. Here we provide the first computation of the power spectrum of biased tracers in redshift space at one loop order, and we make the associated code publicly available. We compare the multipoles \\(\\ell=0,2\\) of the redshift-space halo power spectrum, together with the real-space matter and halo power spectra, with data from numerical simulations at \\(z=0.67\\). For the samples we compare to, which have a number density of \\(\\bar n=3.8 \\cdot 10^{-2}(h \\ {\\rm Mpc}^{-1})^3\\) and \\(\\bar n=3.9 \\cdot 10^{-4}(h \\ {\\rm Mpc}^{-1})^3\\), we find that the calculation at one-loop order matches numerical measurements to within a few percent up to \\(k\\simeq 0.43 \\ h \\ {\\rm Mpc}^{-1}\\), a significant improvement with respect to former techniques. By performing the so-called IR-resummation, we find that the Baryon Acoustic Oscillation peak is accurately reproduced. Based on the results presented here, long-wavelength statistics that are routinely observed in LSS surveys can be finally computed in the EFTofLSS. This formalism thus is ready to start to be compared directly to observational data.

In single-field models of inflation the effect of a long mode with momentum q reduces to a diffeomorphism at zeroth and first order in q. This gives the well-known consistency relations for the n-point functions. At order q^2 the long mode has a physical effect on the short ones, since it induces curvature, and we expect that this effect is the same as being in a curved FRW universe. In this paper we verify this intuition in various examples of the three-point function, whose behaviour at order q^2 can be written in terms of the power spectrum in a curved universe. This gives a simple alternative understanding of the level of non-Gaussianity in single-field models. Non-Gaussianity is always parametrically enhanced when modes freeze at a physical scale k_{ph, f} shorter than H: f_{NL} \\sim (k_{ph, f}/H)^2.