Higgs Mass and Gravity Waves in Standard Model False Vacuum Inflation

In previous publications we have proposed that Inflation can be realized in a second minimum of the Standard Model Higgs potential at energy scales of about $10^{16}$ GeV, if the minimum is not too deep and if a mechanism which allows a transition to the radiation dominated era can be found. This is provided, {\it e.g.}, by scalar-tensor gravity models or hybrid models. Using such ideas we had predicted the Higgs boson mass to be of about $126\pm 3$ GeV, which has been confirmed by the LHC, and that a possibly measurable amount of gravity waves should be produced. Using more refined recent theoretical calculations of the RGE we show that such scenario has the right scale of Inflation only for small Higgs mass, lower than about 124 GeV, otherwise gravity waves are overproduced. The precise value is subject to some theoretical error and to experimental errors on the determination of the strong coupling constant. Such an upper bound corresponds also to the recent claimed measurement by BICEP2 of the scale of inflation through primordial tensor modes. Finally we show that introducing a moderately large non-minimal coupling for the Higgs field the bound can shift to larger values and be reconciled with the LHC measurements of the Higgs mass.Comment: 6 pages, 4 figure

Dissipative Axial Inflation

We analyze in detail the background cosmological evolution of a scalar field coupled to a massless abelian gauge field through an axial term $\frac{\phi}{f_\gamma} F \tilde{F}$, such as in the case of an axion. Gauge fields in this case are known to experience tachyonic growth and therefore can backreact on the background as an effective dissipation into radiation energy density $\rho_R$, which which can lead to inflation without the need of a flat potential. We analyze the system, for momenta $k$ smaller than the cutoff $f_\gamma$, including numerically the backreaction. We consider the evolution from a given static initial condition and explicitly show that, if $f_\gamma$ is smaller than the field excursion $\phi_0$ by about a factor of at least ${\cal O} (20)$, there is a friction effect which turns on before that the field can fall down and which can then lead to a very long stage of inflation with a generic potential. In addition we find superimposed oscillations, which would get imprinted on any kind of perturbations, scalars and tensors. Such oscillations have a period of 4-5 efolds and an amplitude which is typically less than a few percent and decreases linearly with $f_\gamma$. We also stress that the comoving curvature perturbation on uniform density should be sensitive to slow-roll parameters related to $\rho_R$ rather than $\dot{\phi}^2/2$, although we postpone a calculation of the power spectrum and of non-gaussianity to future work and we simply define and compute suitable slow roll parameters. Finally we stress that this scenario may be realized in the axion case, if the coupling $1/f_\gamma$ to U(1) (photons) is much larger than the coupling $1/f_G$ to non-abelian gauge fields (gluons), since the latter sets the range of the potential and therefore the maximal allowed $\phi_0\sim f_G$.Comment: 22 pages, 27 figure

Thermalized Axion Inflation

We analyze the dynamics of inflationary models with a coupling of the inflaton $\phi$ to gauge fields of the form $\phi F \tilde{F}/f$, as in the case of axions. It is known that this leads to an instability, with exponential amplification of gauge fields, controlled by the parameter $\xi= \dot{\phi}/(2fH)$, which can strongly affect the generation of cosmological perturbations and even the background. We show that scattering rates involving gauge fields can become larger than the expansion rate $H$, due to the very large occupation numbers, and create a thermal bath of particles of temperature $T$ during inflation. In the thermal regime, energy is transferred to smaller scales, radically modifying the predictions of this scenario. We thus argue that previous constraints on $\xi$ are alleviated. If the gauge fields have Standard Model interactions, which naturally provides reheating, they thermalize already at $\xi\gtrsim2.9$, before perturbativity constraints and also before backreaction takes place. In absence of SM interactions (i.e. for a dark photon), we find that gauge fields and inflaton perturbations thermalize if $\xi\gtrsim3.4$; however, observations require $\xi\gtrsim6$, which is above the perturbativity and backreaction bounds and so a dedicated study is required. After thermalization, though, the system should evolve non-trivially due to the competition between the instability and the gauge field thermal mass. If the thermal mass and the instabilities equilibrate, we expect an equilibrium temperature of $T_{eq} \simeq \xi H/\bar{g}$ where $\bar{g}$ is the effective gauge coupling. Finally, we estimate the spectrum of perturbations if $\phi$ is thermal and find that the tensor to scalar ratio is suppressed by $H/(2T)$, if tensors do not thermalize.Comment: 36 pages, 6 figures, Published versio

CMB all-scale blackbody distortions induced by linearizing temperature

Cosmic Microwave Background (CMB) experiments, such as WMAP and Planck, measure intensity anisotropies and build maps using a linearized formula for relating them to the temperature blackbody fluctuations. However, this procedure also generates a signal in the maps in the form of y-type distortions which is degenerate with the thermal Sunyaev Zel'dovich (tSZ) effect. These are small effects that arise at second-order in the temperature fluctuations not from primordial physics but from such a limitation of the map-making procedure. They constitute a contaminant for measurements of: our peculiar velocity, the tSZ and primordial y-distortions. They can nevertheless be well-modeled and accounted for. We show that the distortions arise from a leakage of the CMB dipole into the y-channel which couples to all multipoles, mostly affecting the range $\ell$ < ~400. This should be visible in Planck's y-maps with an estimated signal-to-noise ratio of about 12. We note however that such frequency-dependent terms carry no new information on the nature of the CMB dipole. This implies that the real significance of Planck's Doppler coupling measurements is actually lower than reported by the collaboration. Finally, we quantify the level of contamination in tSZ and primordial y-type distortions and show that it is above the sensitivity of proposed next generation CMB experiments.Comment: v3: Some corrections and clarifications, including revised S/N of the effect and a new figure. Matches published version. 8 pages, 4 figure

CMB Aberration and Doppler Effects as a Source of Hemispherical Asymmetries

Our peculiar motion with respect to the CMB rest frame represents a preferred direction in the observed CMB sky since it induces an apparent deflection of the observed CMB photons (aberration) and a shift in their frequency (Doppler). Both effects distort the multipoles $a_{\ell m}$'s at all $\ell$'s. Such effects are real as it has been recently measured for the first time by Planck according to what was forecast in some recent papers. However, the common lore when estimating a power spectrum from CMB is to consider that Doppler affects only the $\ell=1$ multipole, neglecting any other corrections. In this work we use simulations of the CMB sky in a boosted frame with a peculiar velocity $\beta = v/c = 1.23 \times 10^{-3}$ in order to assess the impact of such effect on power spectrum estimations in different regions of the sky. We show that the boost induces a north-south asymmetry in the power spectrum which is highly significant and non-negligible, of about (0.58 $\pm$ 0.10)% for half-sky cuts when going up to $\ell$ = 2500. We suggest that these effects are relevant and may account for some of the north-south asymmetries seen in the Planck data, being especially important at small scales. Finally we analyze the particular case of the ACT experiment, which observed only a small fraction of the sky and show that it suffers a bias of about 1% on the power spectrum and of similar size on some cosmological parameters: for example the position of the peaks shifts by 0.5% and the overall amplitude of the spectrum is about 0.4% lower than a full-sky case.Comment: 13 pages, 5 figure

On the proper kinetic quadrupole CMB removal and the quadrupole anomalies

It has been pointed out recently that the quadrupole-octopole alignment in the CMB data is significantly affected by the so-called kinetic Doppler quadrupole (DQ), which is the temperature quadrupole induced by our proper motion. Assuming our velocity is the dominant contribution to the CMB dipole we have v/c = beta = (1.231 +/- 0.003) * 10^{-3}, which leads to a non-negligible DQ of order beta^2. Here we stress that one should properly take into account that CMB data are usually not presented in true thermodynamic temperature, which induces a frequency dependent boost correction. The DQ must therefore be multiplied by a frequency-averaged factor, which we explicitly compute for several CMB maps finding that it varies between 1.67 and 2.47. This is often neglected in the literature and turns out to cause a small but non-negligible difference in the significance levels of some quadrupole-related statistics. For instance the alignment significance in the SMICA 2013 map goes from 2.3sigma to 3.3sigma, with the frequency dependent DQ, instead of 2.9sigma ignoring the frequency dependence in the DQ. Moreover as a result of a proper DQ removal, the agreement across different map-making techniques is improved.Comment: v2: improvements to the text; 2 figures and several references added; results unchanged. [14 pages, 3 tables, 2 figures

On systematic and GR effects on muon g−2g-2 experiments

We derive in full generality the equations that govern the time dependence of the energy ${\mathcal E}$ of the decay electrons in a muon $g-2$ experiment. We include both electromagnetic and gravitational effects and we estimate possible systematics on the measurements of $g-2\equiv 2(1+a)$, whose experimental uncertainty will soon reach $\Delta a/a\approx 10^{-7}$. In addition to the standard modulation of ${\mathcal E}$ when the motion is orthogonal to a constant magnetic field $B$, with angular frequency $\omega_a=e a |B|/m$, we study effects due to: (1) a non constant muon $\gamma$ factor, in presence of electric fields $E$, (2) a correction due to a component of the muon velocity along $B$ (the `pitch correction'), (3) corrections to the precession rate due to $E$ fields, (4) non-trivial spacetime metrics. Oscillations along the radial and vertical directions of the muon lead to oscillations in ${\mathcal E}$ with a relative size of order $10^{-6}$, for the BNL $g-2$ experiment. We then find a subleading effect in the `pitch' correction, leading to a frequency shift of $\Delta \omega_a/\omega_a \approx {\cal O}(10^{-9})$ and subleading effects of about $\Delta \omega_a/\omega_a \approx {\rm few} \times {\cal O}(10^{-8}-10^{-9})$ due to $E$ fields. Finally we show that GR effects are dominated by the Coriolis force, due to the Earth rotation with angular frequency $\omega_T$, leading to a correction of about $\Delta \omega_a/\omega_a \approx \omega_T/(\gamma \omega_a) \approx {\cal O}(10^{-12})$. A similar correction might be more appreciable for future electron $g-2$ experiments, being of order $\Delta \omega_a/\omega_{a, {\rm el}} \approx \omega_T/(\omega_{a, {\rm el}}) \approx 7\times 10^{-13}$, compared to the present experimental uncertainty, $\Delta a_{\rm el}/a_{\rm el}\approx 10^{-10}$, and forecasted to reach soon $\Delta a_{\rm el}/a_{\rm el}\approx 10^{-11}$.Comment: 37 pages, 6 figure

Standard Model False Vacuum Inflation: Correlating the Tensor-to-Scalar Ratio to the Top Quark and Higgs Boson masses

For a narrow band of values of the top quark and Higgs boson masses, the Standard Model Higgs potential develops a false minimum at energies of about $10^{16}$ GeV, where primordial Inflation could have started in a cold metastable state. A graceful exit to a radiation-dominated era is provided, e.g., by scalar-tensor gravity models. We pointed out that if Inflation happened in this false minimum, the Higgs boson mass has to be in the range $126.0 \pm 3.5$ GeV, where ATLAS and CMS subsequently reported excesses of events. Here we show that for these values of the Higgs boson mass, the inflationary gravitational wave background has be discovered with a tensor-to-scalar ratio at hand of future experiments. We suggest that combining cosmological observations with measurements of the top quark and Higgs boson masses represents a further test of the hypothesis that the Standard Model false minimum was the source of Inflation in the Universe.Comment: v1: 4 pages, 2 figures; v2: 5 pages, 2 figures, improvements in the text; v3: 5 pages, 2 figures, minor improvements in the text, matches PRL versio