Neutrinos and Future Concordance Cosmologies

We review the free parameters in the concordance cosmology, and those which might be added to this set as the quality of astrophysical data improves. Most concordance parameters encode information about otherwise unexplored aspects of high energy physics, up to the GUT scale via the "inflationary sector," and possibly even the Planck scale in the case of dark energy. We explain how neutrino properties may be constrained by future astrophysical measurements. Conversely, future neutrino physics experiments which directly measure these parameters will remove uncertainty from fits to astrophysical data, and improve our ability to determine the global properties of our universe.Comment: Proceedings of paper given at Neutrino 2008 meeting (by RE

Inflation and the Scale Dependent Spectral Index: Prospects and Strategies

We consider the running of the spectral index as a probe of both inflation itself, and of the overall evolution of the very early universe. Surveying a collection of simple single field inflationary models, we confirm that the magnitude of the running is relatively consistent, unlike the tensor amplitude, which varies by orders of magnitude. Given this target, we confirm that the running is potentially detectable by future large scale structure or 21 cm observations, but that only the most futuristic measurements can distinguish between these models on the basis of their running. For any specified inflationary scenario, the combination of the running index and unknown post-inflationary expansion history induces a theoretical uncertainty in the predicted value of the spectral index. This effect can easily dominate the statistical uncertainty with which Planck and its successors are expected to measure the spectral index. More positively, upcoming cosmological experiments thus provide an intriguing probe of physics between TeV and GUT scales by constraining the reheating history associated with any specified inflationary model, opening a window into the "primordial dark age" that follows the end of inflation.Comment: 32 pages. v2 and v3 Minor reference updates /clarification

Primordial Black Holes, Eternal Inflation, and the Inflationary Parameter Space after WMAP5

We consider constraints on inflation driven by a single, minimally coupled scalar field in the light of the WMAP5 dataset, as well as ACBAR and the SuperNova Legacy Survey. We use the Slow Roll Reconstruction algorithm to derive optimal constraints on the inflationary parameter space. The scale dependence in the slope of the scalar spectrum permitted by WMAP5 is large enough to lead to viable models where the small scale perturbations have a substantial amplitude when extrapolated to the end of inflation. We find that excluding parameter values which would cause the overproduction of primordial black holes or even the onset of eternal inflation leads to potentially significant constraints on the slow roll parameters. Finally, we present a more sophisticated approach to including priors based on the total duration of inflation, and discuss the resulting restrictions on the inflationary parameter space.Comment: v2: version published in JCAP. Minor clarifications and references adde

Constraining Inflation

Slow roll reconstruction is derived from the Hamilton-Jacobi formulation of inflationary dynamics. It automatically includes information from sub-leading terms in slow roll, and facilitatesthe inclusion of priors based on the duration on inflation. We show that at low inflationary scales the Hamilton-Jacobi equations simplify considerably. We provide a new classification scheme for inflationary models, based solely on the number of parameters needed to specify the potential, and provide forecasts for likely bounds on the slow roll parameters from future datasets. A minimal running of the spectral index, induced solely by the first two slow roll parameters (\epsilon and \eta) appears to be effectively undetectable by realistic Cosmic Microwave Background experiments. However, we show that the ability to detect this signal increases with the lever arm in comoving wavenumber, and we conjecture that high redshift 21 cm data may allow tests of second order consistency conditions on inflation. Finally, we point out that the second order corrections to the spectral index are correlated with the inflationary scale, and thus the amplitude of the CMB B-mode.Comment: 32 pages. v

Subleading effects and the field range in axion inflation

An attractive candidate for the inflaton is an axion slowly rolling down a flat potential protected by a perturbative shift symmetry. Realisations of this idea within large field, natural and monomial inflation have been disfavoured by observations and are difficult to embed in string theory. We show that subleading, but significant non-perturbative corrections can superimpose sharp cliffs and gentle plateaus into the potential, whose overall effect is to enhance the number of e-folds of inflation. Sufficient e-folds are therefore achieved for smaller field ranges compared to the potential without such corrections. Thus, both single-field natural and monomial inflation in UV complete theories like string theory, can be restored into the favour of current observations, with distinctive signatures. Tensor modes result un-observably small, but there is a large negative running of the spectral index. Remarkably, natural inflation can be achieved with a single field whose axion decay constant is sub-Planckian.Comment: 18 pages, 15 figures; v2 references improve

Can power spectrum observations rule out slow-roll inflation?

The spectral index of scalar perturbations is an important observable that allows us to learn about inflationary physics. In particular, a detection of a significant deviation from a constant spectral index could enable us to rule out the simplest class of inflation models. We investigate whether future observations could rule out canonical single-field slow- roll inflation given the parameters allowed by current observational constraints. We find that future measurements of a constant running (or running of the running) of the spectral index over currently available scales are unlikely to achieve this. However, there remains a large region of parameter space (especially when considering the running of the running) for falsifying the assumed class of slow-roll models if future observations accurately constrain a much wider range of scales

Running Spectral Index and Formation of Primordial Black Hole in Single Field Inflation Models

A broad range of single field models of inflation are analyzed in light of all relevant recent cosmological data, checking whether they can lead to the formation of long-lived Primordial Black Holes (PBHs). To that end we calculate the spectral index of the power spectrum of primordial perturbations as well as its first and second derivatives. PBH formation is possible only if the spectral index increases significantly at small scales, i.e. large wave number $k$. Since current data indicate that the first derivative $\alpha_S$ of the spectral index $n_S(k_0)$ is negative at the pivot scale $k_0$, PBH formation is only possible in the presence of a sizable and positive second derivative ("running of the running") $\beta_S$. Among the three small-field and five large-field models we analyze, only one small-field model, the "running mass" model, allows PBH formation, for a narrow range of parameters. We also note that none of the models we analyze can accord for a large and negative value of $\alpha_S$, which is weakly preferred by current data.Comment: 26 pages, 5 figures, Refs. added, Minor textual change; version to appear in JCA

Higher Order Corrections to the Primordial Gravitational Wave Spectrum and its Impact on Parameter Estimates for Inflation

We study the impact of the use of the power series expression for the primordial tensor spectrum on parameter estimation from future direct detection gravitational wave experiments. The spectrum approximated by the power series expansion may give large deviation from the true (fiducial) value when it is normalized at CMB scale because of the large separation between CMB and direct detection scales. We derive the coefficients of the higher order terms of the expansion up to the sixth order within the framework of the slow-roll approximation and investigate how well the inclusion of higher order terms improves the analytic prediction of the spectrum amplitude by comparing with numerical results. Using the power series expression, we consider future constraints on inflationary parameters expected from direct detection experiments of the inflationary gravitational wave background and show that the truncation of the higher order terms can lead to incorrect evaluation of the parameters. We present two example models; a quadratic chaotic inflation model and mixed inflaton and curvaton model with a quartic inflaton potential.Comment: 25 pages, 7 figures, revised version accepted by JCA

Single-field inflation constraints from CMB and SDSS data

We present constraints on canonical single-field inflation derived from WMAP five year, ACBAR, QUAD, BICEP data combined with the halo power spectrum from SDSS LRG7. Models with a non-scale-invariant spectrum and a red tilt n_s < 1 are now preferred over the Harrison-Zel'dovich model (n_s = 1, tensor-to-scalar ratio r = 0) at high significance. Assuming no running of the spectral indices, we derive constraints on the parameters (n_s, r) and compare our results with the predictions of simple inflationary models. The marginalised credible intervals read n_s = 0.962^{+0.028}_{-0.026} and r < 0.17 (at 95% confidence level). Interestingly, the 68% c.l. contours favour mainly models with a convex potential in the observable region, but the quadratic potential model remains inside the 95% c.l. contours. We demonstrate that these results are robust to changes in the datasets considered and in the theoretical assumptions made. We then consider a non-vanishing running of the spectral indices by employing different methods, non-parametric but approximate, or parametric but exact. With our combination of CMB and LSS data, running models are preferred over power-law models only by a Delta chi^2 ~ 5.8, allowing inflationary stages producing a sizable negative running -0.063^{+0.061}_{-0.049} and larger tensor-scalar ratio r < 0.33 at the 95% c.l. This requires large values of the third derivative of the inflaton potential within the observable range. We derive bounds on this derivative under the assumption that the inflaton potential can be approximated as a third order polynomial within the observable range.Comment: 32 pages, 7 figures. v2: additional references, some typos corrected, passed to JCAP style. v3: minor changes, matches published versio