AR_final file_2018-19

‘brane’) embedded in a five-dimensional spacetime (the ‘bulk’). In this scenario, the matter and gauge fields of the standard model are confined to the brane, while gravity can propagate in the extra dimension. An important class of braneworld models, known as the Dvali–Gabadadze–Porrati (DGP), contains the so-called ‘induced-gravity’ term in the action for the brane, which modifies gravity on relatively large spatial scales. Depending upon the embed- ding of the brane in the bulk space, this model has two branches of cosmological solutions: the ‘self- accelerating’ branch and the ‘normal’ branch. The self-accelerating branch is plagued by the existence of ghost excitations while no ghosts appear on the normal branch. Because of the ghost problem, the self-accelerating branch is of limited interest, while the normal branch is physically viable and consis- tent with current cosmological observations. Varun Sahni and Yuri Shtanov, have shown that the normal branch has a phantom-like effective equation of state w eff < − 1 for dark energy, which serves as a smoking-gun test for this scenario. An important feature of the phantom brane is that its expansion rate is slower than ΛCDM, i.e., H ( z ) | brane < H ( z ) | ΛCDM . This intriguing property allows the braneworld to better account for mea- surements of H ( z ) at z ∼ 2, which appear to be in some tension with ΛCDM. To test braneworld cosmology at the linear per- turbative level, one needs to know the behaviour of matter density perturbations in this model. This is usually described in terms of the growth rate: f ≡ d ln δ m d ln a . where δ m = δρ m /ρ m is the matter density contrast. For the ΛCDM model and for a large variety of dynamical dark energy models with slowly varying w , the growth rate can be approximated as: f = Ω γ m , with Ω m = 8 πGρ m 3 H 2 , where γ is the growth index. For low redshifts, γ is a slowly varying function of z , close to some con- stant γ 0 . The value of γ 0 depends on the equation of state w , and thus the growth index can be used to discriminate between different models of the dy- namical dark energy. For example, when w = − 1 (as in the ΛCDM model), we have γ 0 = 6 / 11. Alexander Viznyuk, Yuri Shtanov, Satadru Bag and Varun Sahni have demonstrated that the traditional parametrization is not successful for the phantom brane. The evolution of the matter density contrast δ m = δρ m /ρ m for the braneworld model in the quasi-static approximation is given by ¨ δ m + 2 H ˙ δ m = g E (4 πGρ m δ m ) , where g E is a time-dependent function that can be regarded as a renormalization factor for the gravi- tational constant. Based on a power series expansion at large red- shifts, they have proposed a versatile parametriza- tion for this model f = Ω γ m 1 + b ℓH β , (3) where γ ≈ 6 / 11 + 0 . 00729 (1 − Ω m ) + α 0 ℓH , α 0 = 0 . 025 , (4) and β = 0 . 084, b = 3 . 383. Figure shows the comparison of the ansatz (3)– (4) with the exact solution obtained by solving () numerically. One finds that the exact solution of f is very well described by the ansatz, the error being of the order 0 . 1% for values of Ω ℓ consistent with the observations. A study of the epoch of reioniza- tion using percolation analysis and Shapefinders The epoch of reionization (EoR) is one of the most important but least understood epochs in the his- tory of our universe. During this epoch, the diffuse hydrogen in the intergalactic medium (IGM) grad- ually changed its state from being neutral (HI) to ionized (HII). Our knowledge about this epoch has been guided so far by observations of the Thomson ( 60 )