Primordial Gravitational Waves with LISA

Primordial Gravitational Waves are the next target of modern cosmology. They represent a window on the early Universe and the only probe of the physics and microphysics of the inflationary period. When the production of GWs happens in scenarios richer than the standard single-field slow-roll, the GW signal becomes potentially detectable also on scales smaller than the Cosmic Microwave Background. LISA will be extremely complementary to CMB experiments to extract information about primordial inflationary models and in particular to probe phases of the inflationary period for which we have very poor knowledges.acceptedVersio

Parity violation in the CMB bispectrum by a rolling pseudoscalar

We investigate parity-violating signatures of temperature and polarization bispectra of the cosmic microwave background (CMB) in an inflationary model where a rolling pseudoscalar produces large equilateral tensor non-Gaussianity. By a concrete computation based on full-sky formalism, it is shown that resultant CMB bispectra have nonzero signals in both parity-even $(\ell_1 + \ell_2 + \ell_3 = {\rm even})$ and parity-odd $(\ell_1 + \ell_2 + \ell_3 = {\rm odd})$ spaces, and are almost uncorrelated with usual scalar-mode equilateral bispectra. These characteristic signatures and polarization information help to detect such tensor non-Gaussianity. Use of both temperature and E-mode bispectra potentially improves of $400\%$ the detectability with respect to an analysis with temperature bispectrum alone. Considering B-mode bispectrum, the signal-to-noise ratio may be able to increase by 3 orders of magnitude. We present the $1\sigma$ uncertainties of a parameter depending on a coupling constant and a rolling condition for the pseudoscalar expected in the ${\it Planck}$ and the proposed PRISM experiments.Comment: 19 pages, 5 figures. Accepted for publication in JCA

The expected anisotropy in solid inflation

Solid inflation is an effective field theory of inflation in which isotropy and homogeneity are accomplished via a specific combination of anisotropic sources (three scalar fields that individually break isotropy). This results in specific observational signatures that are not found in standard models of inflation: a non-trivial angular dependence for the squeezed bispectrum, and a possibly long period of anisotropic inflation (to drive inflation, the "solid" must be very insensitive to any deformation, and thus background anisotropies are very slowly erased). In this paper we compute the expected level of statistical anisotropy in the power spectrum of the curvature perturbations of this model. To do so, we account for the classical background values of the three scalar fields that are generated on large (superhorizon) scales during inflation via a random walk sum, as the perturbation modes leave the horizon. Such an anisotropy is unavoidably generated, even starting from perfectly isotropic classical initial conditions. The expected level of anisotropy is related to the duration of inflation and to the amplitude of the squeezed bispectrum. If this amplitude is close to its current observational limit (so that one of the most interesting predictions of the model can be observed in the near future), we find that a level of statistical anisotropy $\gtrsim 3\%$ in the power spectrum is to be expected, if inflation lasted $\gtrsim 20-30$ e-folds more than the final $50-60$ efolds required to generare the CMB modes. We also comment and point out various similarities between solid inflation and models of inflation where a suitable coupling of the inflaton to a vector kinetic term $F^{2}$ gives frozen and scale invariant vector perturbations on superhorizon scales.Comment: 12 pages, 2 figure

An Hamilton-Jacobi formulation of anisotropic inflation

Classifying inflationary scenarios according to their scaling properties is a powerful way to connect theory with observations. A useful tool to make such a classification is the beta-function formalism. By describing inflation in terms of renormalization group equations, within this framework, it is possible to define universality classes, which can be considered as sets of theories that share a common scale invariant limit. In this paper we apply the formalism to define such classes of universality for models of inflation where the inflaton is coupled to gauge fields. We show that the formalism may consistently be extended to capture the peculiar features of these models such as statistical anisotropy. We also obtain some consistency conditions which serve as useful guidelines for model building.Comment: 29 pages, 1 figure, 2 appendice

Anisotropy in solid inflation

In the model of solid / elastic inflation, inflation is driven by a source that has the field theoretical description of a solid. To allow for prolonged slow roll inflation, the solid needs to be extremely insensitive to the spatial expansion. We point out that, because of this property, the solid is also rather inefficient in erasing anisotropic deformations of the geometry. This allows for a prolonged inflationary anisotropic solution, providing the first example with standard gravity and scalar fields only which evades the conditions of the so called cosmic no-hair conjecture. We compute the curvature perturbations on the anisotropic solution, and the corresponding phenomenological bound on the anisotropy. Finally, we discuss the analogy between this model and the f (phi) F^2 model, which also allows for anisotropic inflation thanks to a suitable coupling between the inflaton phi and a vector field. We remark that the bispectrum of the curvature perturbations in solid inflation is enhanced in the squeezed limit and presents a nontrivial angular dependence, as had previously been found for the f (phi) F^2 model.Comment: 16 pages, 2 figure

CMB statistical anisotropy from noncommutative gravitational waves

Primordial statistical anisotropy is a key indicator to investigate early Universe models and has been probed by the cosmic microwave background (CMB) anisotropies. In this paper, we examine tensor-mode CMB fluctuations generated from anisotropic gravitational waves, parametrised by $P_h({\bf k}) = P_h^{(0)}(k) [ 1 + \sum_{LM} f_L(k) g_{LM} Y_{LM} (\hat{\bf k}) ]$, where $P_h^{(0)}(k)$ is the usual scale-invariant power spectrum. Such anisotropic tensor fluctuations may arise from an inflationary model with noncommutativity of fields. It is verified that in this model, an isotropic component and a quadrupole asymmetry with $f_0(k) = f_2(k) \propto k^{-2}$ are created and hence highly red-tilted off-diagonal components arise in the CMB power spectra, namely $\ell_2 = \ell_1 \pm 2$ in $TT$, $TE$, $EE$ and $BB$, and $\ell_2 = \ell_1 \pm 1$ in $TB$ and $EB$. We find that B-mode polarisation is more sensitive to such signals than temperature and E-mode polarisation due to the smallness of large-scale cosmic variance and we can potentially measure $g_{00} = 30$ and $g_{2M} = 58$ at 68% CL in a cosmic-variance-limited experiment. Such a level of signal may be measured in a PRISM like experiment, while the instrumental noise contaminates it in the $Planck$ experiment. These results imply that it is impossible to measure the noncommutative parameter if it is small enough for the perturbative treatment to be valid. Our formalism and methodology for dealing with the CMB tensor statistical anisotropy are general and straightforwardly applicable to other early Universe models.Comment: 13 pages, 2 figures, 1 table. Accepted for publication in JCA

Anisotropic cosmological solutions in R+R2R + R^2 gravity

In this paper we investigate the past evolution of an anisotropic Bianchi I universe in $R+R^2$ gravity. Using the dynamical system approach we show that there exists a new two-parameters set of solutions that includes both an isotropic "false radiation" solution and an anisotropic generalized Kasner solution, which is stable. We derive the analytic behaviour of the shear from a specific property of $f(R)$ gravity and the analytic asymptotic form of the Ricci scalar when approaching the initial singularity. Finally we numerically checked our results.Comment: 13 pages, 2 figure

Statistical Anisotropy and non-Gaussianity from the Early Universe

Cosmological observations suggest that the universe is homogeneous and isotropic on large scales and that the temperature fluctuations are Gaussian. This has been confirmed by Planck, that measured a level of non-Gaussianity compatible with zero at 68% CL for the primordial local, equilateral and orthogonal bispectrum amplitude . All these observational evidences seem to be in accordance with a scalar-driven inflation epoch in which a scalar field, the inflaton, drives a quasi de Sitter exponential phase of expansion. Nevertheless, Planck measures a nearly scale-invariant spectrum of fluctuations . This nearly scale-invariance suggests that the time-traslational symmetry is slightly broken during inflation. So it becomes natural to ask if other symmetries are also broken and what are the observational consequences. Furthermore, the evidence of some ‘anomalies’, previously observed in the WMAP data and now confirmed (at similar level of significance) by Planck, suggests a possible violation of some symmetries at some point in the evolution of the universe, possibly at very early times. Different anomalies have been observed: a quadrupole-octupole alignment, a dipolar power asymmetry and also an hemispherical asymmetry in power between the northern and southern hemisphere. These features suggest a possible violation of statistical isotropy and/or of parity invariance. Invariance under spatial rotations and parity transformations remains unbroken in the usual inflation models based on scalar fields, so it is necessary to modify the matter content of primordial universe introducing new field(s) or assuming new configuration pattern for the background field that differs from the usual time-dependent background scalar field one. Motivated by these observations, theoretical models that can sustain anisotropic phase of expansion can have an active role and generate statistical anisotropy in primordial fluctuations. This can be realized by introducing gauge field coupled with scalar and/or pseudoscalar fields or by considering three scalar fields in anisotropic background with an unusual breaking pattern of spacetime symmetries that does not involve breaking of time translations. Breaking of rotational symmetry implies that the correlation functions exhibit a direction dependence and, in particular, the two-point correlation function in Fourier space (power spectrum) of primordial curvature perturbations defined by $\langle\zeta_{k_{1}} \zeta_{k_{2}}\rangle=\left(2\pi\right)^3 \delta^{(3)}\left(\textbf{k}_{1}+\textbf{k}_{2}\right)P_{\zeta}\left(\textbf{k}_{1}\right)$ is modified as Pζ(k) =Piso (k) [1+ g* (k)( k°n)] where Piso (k) is the isotropic power spectrum, n is a space preferred direction and g* is a parameter characterizing the amplitude of violation of rotational symmetry. Within the context of primordial anisotropic models we have developed this Ph.D thesis and in particular we have analyzed a model in which a suitable coupling of the inflaton ᶲ to a vector kinetic term F2 generates an anisotropic power spectrum and a bispectrum with a non-trivial angular dependence in the squeezed limit. In particular we have found that an anisotropy amplitude g* of order 1% (10%) is possible if inflation lasted ~5 (~50) e-folds more than the usual 60 required to produce the CMB modes. One of the most important results found in this analysis concerns the presence of infrared modes of the perturbations of the gauge field. These infrared modes determine a classical vector field that tends to raise the level of statistical anisotropy to levels very close to the observational limits. Peculiar predictions of this model are TB and EB mixing between temperature and polarizations modes in the CMB due to the anisotropy and a correlation between the anisotropy in power spectrum g* and the amplitude of the bispectrum fNL that can be considered a consistency relation for all these kind of models that break the rotational invariance. Always in the aim of isotropy violation, but with a completely different approach that involves a scalar fields model, later we have shown, for the first time, how with standard gravity and scalar fields only, is possible to evades the conditions of the cosmic no-hair conjecture. In this model, dubbed solid / elastic model, inflation is driven by a solid. A prolonged slow-roll period of acceleration is guaranteed by the extreme insensibility of the solid to the spatial expansion. We point out that, because of this property, the solid is also rather inefficient in erasing anisotropic deformations of the geometry. This allows for a prolonged inflationary anisotropic solution and for a generation of a non-negligible amount of anisotropy g* in the power spectrum. Finally we have investigated parity-violating signatures of temperature and polarization bispectra of the cosmic microwave background (CMB) in an inflationary model where a rolling pseudoscalar, coupled with a vector field, produces large equilateral tensor non-Gaussianity. We have shown that the possibility to use polarization information and the parity-even and parity-odd l-space improves of many order of magnitude the detectability of such bispectra with respect to an analysis with only temperature. Considering the progressive improvements in accuracy of the next cosmological surveys it is useful to introduce and analyze particular tools, like statistical anisotropy, parity violation, new shapes of non-Gaussianity, that can help to discriminate between the plethora of primordial inflationary models

Measuring parity violation in the Stochastic Gravitational Wave Background with the LISA-Taiji network

Parity violation is a powerful observable to distinguish a cosmological background of Gravitational Waves (GWs) from an astrophysical one. Planar single GW interferometers, both on ground and in space, are unable to measure the net circular polarization of an isotropic Stochastic Gravitational Wave Background (SGWB). In this paper, we explore the possibility of detecting circular polarization of an isotropic SGWB by cross-correlating two space-based detectors planned to be launched around 2034: LISA and Taiji. We compute the response of such a network to chirality and we perform a Fisher forecast analysis on the $I$ and $V$ Stokes parameters for the SGWB. We find that a clear measurement of chirality can be claimed for a maximally chiral signal with $h^2 \, \Omega_{\rm GW} \simeq 10^{-12}$.Comment: 22 pages, 4 figure

Non-Gaussianity from the Cross-correlation of the Astrophysical Gravitational Wave Background and the Cosmic Microwave Background

Since the first LIGO/Virgo detection, Gravitational Waves (GWs) have been very promising as a new complementary probe to understand our Universe. One of the next challenges of GW search is the detection and characterization of the stochastic gravitational wave background (SGWB), that is expected to open a window on the very early Universe (cosmological background) and to provide us new information on astrophysical source populations (astrophysical background). One way to characterize the SGWB and to extract information about its origin is through the cross-correlation with other cosmological probes. To this aim, in this paper, we explore the cross-correlation between the astrophysical background anisotropies and the Cosmic Microwave Background (CMB) ones. Such a signal is sensitive to primordial non-Gaussianity (nG) through the GW bias. Thus, we study the capability of next generation space-based interferometers to detect such a cross-correlation signal and to constrain primordial nG.Comment: 13 pages, 5 figure