We consider the Abelian Higgs model in the broken phase as a spectator in cosmological spaces of general $D$ space-time dimensions, and allow for the condensate to be time-dependent. We fix the unitary gauge using Dirac's formalism for constrained systems, and then quantize the gauge-fixed system. Vector and scalar perturbations develop time-dependent masses. We work out their propagators assuming the cosmological background is that of power-law inflation, characterized by a constant principal slow-roll parameter, and that the scalar condensate is in the attractor regime, scaling as the Hubble rate. Our propagators correctly reduce to known results in the Minkowski and de Sitter space limits. We use the vector propagator to compute the equal-time correlators of electric and magnetic fields and find that at super-Hubble separations the former is enhanced, while the latter is suppressed compared to the vacuum fluctuations of the massless vector field. These correlators satisfy the hierarchy governed by Faraday's law.
We study the power spectrum of quasi-single field inflation where strong coupling is considered. The contribution from the massive propagator can be divided into local and non-local contributions. The local one is the leading contribution and is power-law suppressed as a function of mass, while the non-local contribution is exponentially suppressed in the large mass limit. For the local contribution, it is possible to use the effective field theory approach to study the power spectrum in the strongly coupled region of the parameter space. For the non-local contribution, we developed a partial …
I study the "general" case that arises in the Extended Effective Field Theory of Inflation (gEEFToI), in which the coefficients of the sixth order polynomial dispersion relation depend on the physical wavelength of the fluctuation mode, hence they are time-dependent. At arbitrarily short wavelengths the unitarity is lost for each mode. Depending on the values of the gEEFToI parameters in the unitary gauge action, two scenarios can arise: in one, the coefficients of the polynomial become singular, flip signs at some physical wavelength and asymptote to a constant value as the wavelength of the …
We make a proposal for gauge-invariant observables in perturbative quantum gravity in cosmological spacetimes, building on the recent work of Brunetti et al. [JHEP 08 (2016) 032]. These observables are relational, and are obtained by evaluating the field operator in a field-dependent coordinate system. We show that it is possible to define this coordinate system such that the non-localities inherent in any higher-order observable in quantum gravity are causal, i.e., the value of the gauge-invariant observable at a point $x$ only depends on the metric and inflation perturbations in the past lig…
We continue the study of inflationary fluctuations in Holographic Space Time models of inflation. We argue that the holographic theory of inflation provides a physical context for what is often called dS/CFT. The holographic theory is a quantum theory which, in the limit of a large number of e-foldings, gives rise to a field theory on $S^3$, which is the representation space for a unitary representation of SO(1,4). This is not a conventional CFT, and we do not know the detailed non-perturbative axioms for correlation functions. However, the two- and three-point functions are completely determi…
We construct the graviton propagator on de Sitter background in exact de Donder gauge. We prove that it must break de Sitter invariance, just like the propagator of the massless, minimally coupled scalar. Our explicit solutions for its two scalar structure functions preserve spatial homogeneity and isotropy so that the propagator can be used within the larger context of inflationary cosmology, however, it is simple to alter the residual symmetry. Because our gauge condition is de Sitter invariant (although no solution for the propagator can be) renormalization should be simpler using this prop…
Inflationary cosmology attempts to provide a natural explanation for the flatness and homogeneity of the observable universe. In the context of reversible (unitary) evolution, this goal is difficult to satisfy, as Liouville's theorem implies that no dynamical process can evolve a large number of initial states into a small number of final states. We use the invariant measure on solutions to Einstein's equation to quantify the problems of cosmological fine-tuning. The most natural interpretation of the measure is the flatness problem does not exist; almost all Robertson-Walker cosmologies are s…
We study the correction to the scale invariant power spectrum of a scalar field on de Sitter space from small black holes that formed during a pre-inflationary matter dominated era. The formation probability of such black holes is estimated from primordial Gaussian density fluctuations. We determine the correction to the spectrum by first deriving the Keldysh propagator for a massless scalar field on Schwarzschild-de Sitter space. Our results suggest that the effect is strong enough to be tested -- and possibly even ruled out -- by observations.
We study the consequences of (beyond) positivity of scattering amplitudes in the effective field theory description of the Higgs-Dilaton inflationary model. By requiring the EFT to be compatible with a unitary, causal, local and Lorentz invariant UV completion, we derive constraints on the Wilson coefficients of the first higher order derivative operators. We show that the values allowed by the constraints are consistent with the phenomenological applications of the Higgs-Dilaton model.
We show that the Standard Model vacuum can be stabilized if all particle propagators are non-minimally coupled to gravity. This is due to a Higgs-background dependent redefinition of the Standard Model fields: in terms of canonical variables and in the large Higgs field limit, the quantum fluctuations of the redefined fields are suppressed by the Higgs background. Thus, in this regime, quantum corrections to the tree-level electroweak potential are negligible. Finally, we show that in this framework the Higgs boson can be responsible for inflation. Due to a numerical coincidence that originate…
We show how the choice of an inflationary state that entangles scalar and tensor fluctuations affects the angular two-point correlation functions of the $T$, $E$, and $B$ modes of the cosmic microwave background. The propagators for a state starting with some general quadratic entanglement are solved exactly, leading to predictions for the primordial scalar-scalar, tensor-tensor, and scalar-tensor power spectra. These power spectra are expressed in terms of general functions that describe the entangling structure of the initial state relative to the standard Bunch-Davies vacuum. We illustrate …
Higgs inflation is known to be a minimal extension of the Standard Model allowing for the description of the early Universe inflation. This model is considered as an effective field theory since it has a relatively low cutoff scale, thus requiring further extensions to be a valid description of the reheating phase. We present a novel unified approach to the problem of unitarization and UV completion of the Higgs inflation model without introducing new massive degrees of freedom. This approach is based on an analytic infinite derivative modification of the Higgs field kinetic term. We construct…
Propagator positivity bounds for cosmological correlators
Leung Center for Cosmology and Particle Astrophysics, National Taiwan University（国立台湾大学梁中心宇宙学与粒子天体物理学）；Department of Physics and Astronomy, Queen Mary University of London（伦敦玛丽女王大学物理与天文系）
The most general four-derivative Unitary String Effective Action with Torsion and Stringy-Running-Vacuum-Model Inflation: Old ideas from a modern perspective
National Technical University of Athens（雅典国立技术大学）；King’s College London（伦敦国王学院）
In this paper we show that the Germani-Kehagias model of Higgs inflation (or New Higgs Inflation), where the Higgs boson is kinetically non-minimally coupled to the Einstein tensor is in perfect compatibility with the latest Planck and BICEP2 data. Moreover, we show that the tension between the Planck and BICEP2 data can be relieved within the New Higgs inflation scenario by a negative running of the spectral index. Regarding the unitarity of the model, we argue that it is unitary throughout the evolution of the Universe. Weak couplings in the Higgs-Higgs and Higgs-graviton sectors are provide…
We consider the UV-protected inflation, where the inflaton potential is obtained by quantum (one-loop) breaking of a global symmetry into a discrete symmetry. In this model, all coupling scales are sub-Planckian. This is achieved by coupling the inflaton kinetic term to the Einstein tensor such that the friction is enhanced gravitationally at high energies. In this respect, this new interaction makes virtually any potential adequate for inflation while keeping the system perturbative unitary. We show that even if the gravitationally enhanced friction intrinsically contains new nonlinearities, …
The propagator which evolves the wave-function in NRQM, can be expressed as a matrix element of a time evolution operator: i.e $ G_{\rm NR}(x)= \langle{\mathbf{x}_2}|{U_{\rm NR}(t)}|{\mathbf{x}_1}\rangle$ in terms of the orthonormal eigenkets $|{\mathbf{x}}\rangle$ of the position operator. In QFT, it is not possible to define a conceptually useful single-particle position operator or its eigenkets. It is also not possible to interpret the relativistic (Feynman) propagator $G_R(x)$ as evolving any kind of single-particle wave-functions. In spite of all these, it is indeed possible to express t…
We continue developing cosmological models involving nilpotent chiral superfields, which provide a simple unified description of inflation and the current acceleration of the universe in the supergravity context. We describe here a general class of models with a positive cosmological constant at the minimum of the potential, such that supersymmetry is spontaneously broken in the direction of the nilpotent superfield $S$. In the unitary gauge, these models have a simple action where all highly non-linear fermionic terms of the classical Volkov-Akulov action disappear. We present masses for boso…
Very few explicit inflationary scenarios are known to generate a large bispectrum of orthogonal shape. Dirac-Born-Infeld Galileon inflation, in which an induced gravity term is added to the DBI action, is one such model. We formulate it in the language of the effective field theory of inflation by identifying the unitary gauge operators that govern the behavior of its cosmological fluctuations. We show how to recover rather easily from this its power spectrum and bispectrum, which we calculated previously using standard cosmological perturbation theory. We push our calculations up to the deter…
We make use of the frame and gauge independent formalism for scalar and tensor cosmological perturbations developed in Ref. [1] to show that the physical cutoff for 2-to-2 tree level scatterings in Higgs inflation is above the Planck scale M_P throughout inflation. More precisely, we found that in the Jordan frame, the physical cutoff scale is $(Λ/a)_J \gtrsim \sqrt{M_P^2+ξϕ^2}$, while in the Einstein frame it is $(Λ/a)_J \gtrsim M_P$, where $ξ$ is the nonminimal coupling and $ϕ$ denotes the Higgs vev during inflation. The dimensionless ratio of the physical cutoff to the relevant Planck scale…
This thesis presents a possible inflation scenario as a consequence of non-minimal gravitational couplings in the Conformal Standard Model. That model consists, in comparison to the SM, of additional right-chiral neutrinos and a complex scalar sextet which, in distinction to the Higgs boson, is not coupled to the SM particles. The inflation is driven by two non-minimally coupled fields. One of those is the SU(2) Higgs-like doublet and the second is associated with the trace of the sextet. These two fields are related to the Higgs particle and ``shadow'', heavier Higgs via the mass mixing matri…
We provide a compact and unified treatment of power spectrum observables for the effective field theory (EFT) of inflation with the complete set of operators that lead to second-order equations of motion in metric perturbations in both space and time derivatives, including Horndeski and GLPV theories. We relate the EFT operators in ADM form to the four additional free functions of time in the scalar and tensor equations. Using the generalized slow roll formalism, we show that each power spectrum can be described by an integral over a single source that is a function of its respective sound hor…
Light scalars in inflationary spacetimes suffer from logarithmic infrared divergences at every order in perturbation theory. This corresponds to the scalar field values in different Hubble patches undergoing a random walk of quantum fluctuations, leading to a simple toy "landscape" on superhorizon scales, in which we can explore questions relevant to eternal inflation. However, for a sufficiently long period of inflation, the infrared divergences appear to spoil computability. Some form of renormalization group approach is thus motivated to resum the log divergences of conformal time. Such a r…
The theory of holographic space-time (HST) generalizes both string theory and quantum field theory. It provides a geometric rationale for supersymmetry (SUSY) and a formalism in which super-Poincare invariance follows from Poincare invariance. HST unifies particles and black holes, realizing both as excitations of non-commutative geometrical variables on a holographic screen. Compact extra dimensions are interpreted as finite dimensional unitary representations of super- algebras, and have no moduli. Full field theoretic Fock spaces, and continuous moduli are both emergent phenomena of super-P…
As previously discussed in (D. Sudarsky, Int.J.Mod.Phys.D20:509-552, (2011); [arXiv:0906.0315]), the inflationary account for the emergence of the seeds of cosmic structure falls short of actually explaining the generation of primordial anisotropies and inhomogeneities. This description starts from a symmetric background, and invokes symmetric dynamics, so it cannot explain asymmetries. To generate asymmetries, we present an application of the Continuous Spontaneous Localization (CSL) model of wave function collapse (P. Pearle, Phys. Rev. A 39, 2277, (1989); G. C. Ghirardi, P. Pearle and A. Ri…
In a full solution for a scalar quantum field coupled to an accelerating isotropic universe, all constituent non-autonomous modes of elementary excitation cease to oscillate and become unstable at a discrete sequence of times. After canonical quantization the time-frozen Hamiltonian has eigenstates that can be viewed as neither particles nor oscillatory radiation. Under standard canonical quantization, the Hamiltonian has a natural time dependent partitioning into a light component and a dark component. Under equipartition of energy, the energy density of the dark component remains constant. T…
