Inverse problem: Reconstruction of modified gravity action in Palatini formalism by Supernova Type Ia data

We introduce in $f(R)$ gravity--Palatini formalism the method of inverse problem to extract the action from the expansion history of the universe. First, we use an ansatz for the scale factor and apply the inverse method to derive an appropriate action for the gravity. In the second step we use the Supernova Type Ia data set from the Union sample and obtain a smoothed function for the Hubble parameter up to the redshift~1.7. We apply the smoothed Hubble parameter in the inverse approach and reconstruct the corresponding action in $f(R)$ gravity. In the next step we investigate the viability of reconstruction method, doing a Monte-Carlo simulation we generate synthetic SNIa data with the quality of union sample and show that roughly more than 1500 SNIa data is essential to reconstruct correct action. Finally with the enough SNIa data, we propose two diagnosis in order to distinguish between the $\Lambda$CDM model and an alternative theory for the acceleration of the universe.Comment: 8 pages, 8 figures, accepted in Phys. Rev.

A model-independent dark energy reconstruction scheme using the geometrical form of the luminosity-distance relation

We put forward a new model-independent reconstruction scheme for dark energy which utilises the expected geometrical features of the luminosity-distance relation. The important advantage of this scheme is that it does not assume explicit ansatzes for cosmological parameters but only some very general cosmological properties via the geometrical features of the reconstructed luminosity-distance relation. Using the recently released supernovae data by the Supernova Legacy Survey together with a phase space representation, we show that the reconstructed luminosity-distance curves best fitting the data correspond to a slightly varying dark energy density with the Universe expanding slightly slower than the Lambda CDM model. However, the Lambda CDM model fits the data at 1 sigma significance level and the fact that our best fitting luminosity-distance curve is lower than that of the corresponding Lambda CDM model could be due to systematics. The transition from an accelerating to a decelerating expansion occurs at a redshift larger than z=0.35. Interpreting the dark energy as a minimally coupled scalar field we also reconstruct the scalar field and its potential. We constrain $\Omega_{m_0}$ using the baryon acoustic oscillation peak in the SDSS luminous red galaxy sample and find that the best fit is obtained with $\Omega_{m_0}=0.27$, in agreement with the CMB data.Comment: 10 pages, 18 figure

Crossing Statistic: Bayesian interpretation, model selection and resolving dark energy parametrization problem

By introducing Crossing functions and hyper-parameters I show that the Bayesian interpretation of the Crossing Statistics [1] can be used trivially for the purpose of model selection among cosmological models. In this approach to falsify a cosmological model there is no need to compare it with other models or assume any particular form of parametrization for the cosmological quantities like luminosity distance, Hubble parameter or equation of state of dark energy. Instead, hyper-parameters of Crossing functions perform as discriminators between correct and wrong models. Using this approach one can falsify any assumed cosmological model without putting priors on the underlying actual model of the universe and its parameters, hence the issue of dark energy parametrization is resolved. It will be also shown that the sensitivity of the method to the intrinsic dispersion of the data is small that is another important characteristic of the method in testing cosmological models dealing with data with high uncertainties.Comment: 14 pages, 4 figures, discussions extended, 1 figure and two references added, main results unchanged, matches the final version to be published in JCA

Is cosmic acceleration slowing down?

We investigate the course of cosmic expansion in its `recent past' using the Constitution SN Ia sample (which includes CfA data at low redshifts), jointly with signatures of baryon acoustic oscillations (BAO) in the galaxy distribution and fluctuations in the cosmic microwave background (CMB). Earlier SN Ia data sets could not address this issue because of a paucity of data at low redshifts. Allowing the equation of state of dark energy (DE) to vary, we find that a coasting model of the universe (q_0=0) fits the data about as well as LCDM. This effect, which is most clearly seen using the recently introduced `Om' diagnostic, corresponds to an increase of Om(z) and q(z) at redshifts z \lleq 0.3. In geometrical terms, this suggests that cosmic acceleration may have already peaked and that we are currently witnessing its slowing down. The case for evolving DE strengthens if a subsample of the Constitution set consisting of SNLS+ESSENCE+CfA SN Ia data is analysed in combination with BAO+CMB using the same statistical methods. The effect we observe could correspond to DE decaying into dark matter (or something else). A toy model which mimics this process agrees well with the combined SN Ia+BAO+CMB data.Comment: 6 pages, 5 figures, presentation expanded, results for a new subsample of the Constitution set are added, new BAO data are accounted for, main results unchange

Primordial features and Planck polarization

With the Planck 2015 Cosmic Microwave Background (CMB) temperature and polarization data, we search for possible features in the primordial power spectrum (PPS). We revisit the Wiggly Whipped Inflation (WWI) framework and demonstrate how generation of some particular primordial features can improve the fit to Planck data. WWI potential allows the scalar field to transit from a steeper potential to a nearly flat potential through a discontinuity either in potential or in its derivatives. WWI offers the inflaton potential parametrizations that generate a wide variety of features in the primordial power spectra incorporating most of the localized and non-local inflationary features that are obtained upon reconstruction from temperature and polarization angular power spectrum. At the same time, in a single framework it allows us to have a background parameter estimation with a nearly free-form primordial spectrum. Using Planck 2015 data, we constrain the primordial features in the context of Wiggly Whipped Inflation and present the features that are supported both by temperature and polarization. WWI model provides more than $13$ improvement in $\chi^2$ fit to the data with respect to the best fit power law model considering combined temperature and polarization data from Planck and B-mode polarization data from BICEP and Planck dust map. We use 2-4 extra parameters in the WWI model compared to the featureless strict slow roll inflaton potential. We find that the differences between the temperature and polarization data in constraining background cosmological parameters such as baryon density, cold dark matter density are reduced to a good extent if we use primordial power spectra from WWI. We also discuss the extent of bispectra obtained from the best potentials in arbitrary triangular configurations using the BI-spectra and Non-Gaussianity Operator (BINGO).Comment: v1: 22 pages, 7 figures and 1 table; v2: 23 pages, 7 figures and 1 table, minor changes, references added, matches published version in JCA

Two new diagnostics of dark energy

We introduce two new diagnostics of dark energy (DE). The first, Om, is a combination of the Hubble parameter and the cosmological redshift and provides a "null test" of dark energy being a cosmological constant. Namely, if the value of Om(z) is the same at different redshifts, then DE is exactly cosmological constant. The slope of Om(z) can differentiate between different models of dark energy even if the value of the matter density is not accurately known. For DE with an unevolving equation of state, a positive slope of Om(z) is suggestive of Phantom (w < -1) while a negative slope indicates Quintessence (w > -1). The second diagnostic, "acceleration probe"(q-probe), is the mean value of the deceleration parameter over a small redshift range. It can be used to determine the cosmological redshift at which the universe began to accelerate, again without reference to the current value of the matter density. We apply the "Om" and "q-probe" diagnostics to the Union data set of type Ia supernovae combined with recent data from the cosmic microwave background (WMAP5) and baryon acoustic oscillations.Comment: 14 pages, 9 figures. Some new results and an additional reference. Main conclusions unchanged. Matches published versio

Wiggly Whipped Inflation

Motivated by BICEP2 results on the CMB polarization B-mode which imply primordial gravitational waves are produced when the Universe has the expansion rate of about $H \approx 10^{14}$ GeV, and by deviations from a smooth power-law behaviour for multipoles $\ell <50$ in the CMB temperature anisotropy power spectrum found in the WMAP and Planck experiments, we have expanded our class of large field inflationary models that fit both the BICEP2 and Planck CMB observations consistently. These best-fitted large field models are found to have a transition from a faster roll to the slow roll $V(\phi)=m^2 \phi^2/2$ inflation at a field value around 14.6~${\rm M_{Pl}}$ and thus a potential energy of $V(\phi) \sim (10^{16}\,{\rm GeV})^4$. In general this transition with sharp features in the inflaton potential produces not only suppression of scalars relative to tensor modes at small $k$ but also introduces wiggles in the primordial perturbation spectrum. These wiggles are shown to be useful to explain some localized features in the CMB angular power spectrum and can also have other observational consequences. Thus, primordial GW can be used now to make a tomography of inflation determining its fine structure. The resulting Wiggly Whipped Inflation scenario is described in details and the anticipated perturbation power spectra, CMB power spectra, non-Gaussianity and other observational consequences are calculated and compared to existing and forthcoming observations.Comment: 23 pages, 6 figures, 1 table, matches final version published in JCA

Whipped inflation

Motivated by the idea that inflation occurs at the GUT symmetry breaking scale, in this paper we construct a new class of large field inflaton potentials where the inflaton starts with a power law potential; after initial period of relative fast roll that lasts until after a few e-folds inside the horizon, it transits to the attractor of the slow roll part of the potential with a lower power. Due to the initial fast roll stages of inflation, we find a suppression in scalar primordial power at large scales and at the same time the choice of the potential can provide us a tensor primordial spectrum with high amplitude. This suppression in scalar power with a large tensor-to-scalar ratio helps us to reconcile the Planck and BICEP2 data in a single framework. We find that a transition from a cubic to quadratic form of inflaton potential generates an appropriate suppression in power of scalar primordial spectrum that provides significant improvement in fit compared to power law model when compared with Planck and BICEP2 data together. We calculate the extent of non-Gaussianity, specifically, the bispectrum for the best fit potential and show that it is consistent with Planck bispectrum constraints.Comment: 5 pages, 2 figures and 1 table; matches final version published in PR