Leonardo Senatore

The Effective Field Theory of Inflation

We study the effective field theory of inflation, i.e. the most general theory describing the fluctuations around a quasi de Sitter background, in the case of single field models. The scalar mode can be eaten by the metric by going to unitary gauge. In this gauge, the most general theory is built with the lowest dimension operators invariant under spatial diffeomorphisms, like g00 and Kμν, the extrinsic curvature of constant time surfaces. This approach allows us to characterize all the possible high energy corrections to simple slow-roll inflation, whose sizes are constrained by experiments. Also, it describes in a common language all single field models, including those with a small speed of sound and Ghost Inflation, and it makes explicit the implications of having a quasi de Sitter background. The non-linear realization of time diffeomorphisms forces correlation among different observables, like a reduced speed of sound and an enhanced level of non-Gaussianity.

Non-Gaussianities in single field inflation and their optimal limits from the WMAP 5-year data

Using the recently developed effective field theory of inflation, we argue that the size and the shape of the non-Gaussianities generated by single-field inflation are generically well described by two parameters: fNLequil, which characterizes the size of the signal that is peaked on equilateral configurations, and fNLorthog, which instead characterizes the size of the signal which is peaked both on equilateral configurations and flat-triangle configurations (with opposite signs). The shape of non-Gaussianities associated with fNLorthog is orthogonal to the one associated to fNLequil, and former analysis have been mostly blind to it. We perform the optimal analysis of the WMAP 5-year data for both of these parameters. We find no evidence of non-Gaussianity, and we have the following constraints: −125 ≤ fNLequil ≤ 435, −369 ≤ fNLorthog ≤ 71 at 95% CL. We show that both of these constraints can be translated into limits on parameters of the Lagrangian of single-field inflation. For one of them, the speed of sound of the inflaton fluctuations, we find that it is either bounded to be cs ≥ 0.011 at 95% CL. or alternatively to be so small that the higher-derivative kinetic term dominate at horizon crossing. We are able to put similar constraints on the other operators of the inflaton Lagrangian.

A smooth bouncing cosmology with scale invariant spectrum

We present a bouncing cosmology which evolves from the contracting to the expanding phase in a smooth way, without developing instabilities or pathologies and remaining in the regime of validity of 4D effective field theory. A nearly scale invariant spectrum of perturbations is generated during the contracting phase by an isocurvature scalar with a negative exponential potential and then converted to adiabatic. The model predicts a slightly blue spectrum, , no observable gravitational waves and a high (but model dependent) level of non-Gaussianities with local shape. The model represents an explicit and predictive alternative to inflation, although, at present, it is clearly less compelling.

Cosmological Non-Linearities as an Effective Fluid

The universe is smooth on large scales but very inhomogeneous on small scales. Why is the spacetime on large scales modeled to a good approximation by the Friedmann equations? Are we sure that small-scale non-linearities do not induce a large backreaction? Related to this, what is the effective theory that describes the universe on large scales? In this paper we make progress in addressing these questions. We show that the effective theory for the long-wavelength universe behaves as a viscous fluid coupled to gravity: integrating out short-wavelength perturbations renormalizes the homogeneous background and introduces dissipative dynamics into the evolution of long-wavelength perturbations. The effective fluid has small perturbations and is characterized by a few parameters like an equation of state, a sound speed and a viscosity parameter. These parameters can be matched to numerical simulations or fitted from observations. We find that the backreaction of small-scale non-linearities is very small, being suppressed by the large hierarchy between the scale of non-linearities and the horizon scale. The effective pressure of the fluid is always positive and much too small to significantly affect the background evolution. Moreover, we prove that virialized scales decouple completely from the large-scale dynamics, at all orders in the post-Newtonian expansion. We propose that our effective theory be used to formulate a well-defined and controlled alternative to conventional perturbation theory, and we discuss possible observational applications. Finally, our way of reformulating results in second-order perturbation theory in terms of a long-wavelength effective fluid provides the opportunity to understand non-linear effects in a simple and physically intuitive way.

On the consistency relation of the three-point function in single-field inflation

The consistency relation for the three-point function of the cosmic microwave background is a very powerful observational signature which is believed to be true for every inflationary model in which there is only one dynamical degree of freedom. Its importance relies on the fact that deviations from it might be detected in next generation experiments, allowing us to rule out all single-field inflationary models. After making more precise the already existing proof of the consistency relation, we use a recently developed effective field theory for inflationary perturbations to provide an alternative and very explicit proof valid at leading non-trivial order in slow roll parameters.

The effective field theory of multifield inflation

A bstractWe generalize the Effective Field Theory of Inflation to include additional light scalar degrees of freedom that are in their vacuum at the time the modes of interest are crossing the horizon. In order to make the scalars light in a natural way we consider the case where they are the Goldstone bosons of a global symmetry group or are partially protected by an approximate supersymmetry. We write the most general Lagrangian that couples the scalar mode associated to the breaking of time translation during inflation to the additional light scalar fields. This Lagrangian is constrained by diffeomorphism invariance and the additional symmetries that keep the new scalars light. This Lagrangian describes the fluctuations around the time of horizon crossing and it is supplemented with a general parameterization describing how the additional fluctuating fields can affect cosmological perturbations. We find that multifield inflation can reproduce the non-Gaussianities that can be generated in single field inflation but can also give rise to new kinds of non-Gaussianities. We find several new three-point function shapes. We show that in multifield inflation it is possible to naturally suppress the three-point function making the four-point function the leading source of detectable non-Gaussianities. We find that under certain circumstances, i.e. if specific shapes of non-Gaussianities are detected in the data, one could distinguish between single and multifield inflation and sometimes even among the various mechanisms that kept the additional fields light.

The Effective Field Theory of Cosmological Large Scale Structures

A bstractLarge scale structure surveys will likely become the next leading cosmological probe. In our universe, matter perturbations are large on short distances and small at long scales, i.e. strongly coupled in the UV and weakly coupled in the IR. To make precise analytical predictions on large scales, we develop an effective field theory formulated in terms of an IR effective fluid characterized by several parameters, such as speed of sound and viscosity. These parameters, determined by the UV physics described by the Boltzmann equation, are measured from N-body simulations. We find that the speed of sound of the effective fluid is

Optimal limits on fNLlocal from WMAP 5-year data

c_s^2 \approx {1}{0^{{ - {6}}}}{c^{2}}

The cosmological Higgstory of the vacuum instability

and that the viscosity contributions are of the same order. The fluid describes all the relevant physics at long scales k and permits a manifestly convergent perturbative expansion in the size of the matter perturbations δ(k) for all the observables. As an example, we calculate the correction to the power spectrum at order δ(k)4. The predictions of the effective field theory are found to be in much better agreement with observation than standard cosmological perturbation theory, already reaching percent precision at this order up to a relatively short scale k ⋍ 0.24h Mpc−1.

On Loops in Inflation

We have applied the optimal estimator for fNLlocal to the 5 year WMAP data. Marginalizing over the amplitude of foreground templates we get −4 < fNLlocal < 80 at 95% CL. Error bars of previous (sub-optimal) analyses are roughly 40% larger than these. The probability that a Gaussian simulation, analyzed using our estimator, gives a result larger in magnitude than the one we find is 7 %. Our pipeline gives consistent results when applied to the three and five year WMAP data releases and agrees well with the results from our own sub-optimal pipeline. We find no evidence of any residual foreground contamination.