We present a detailed study of cosmological effects of homogeneous tachyon matter coexisting with non-relativistic matter and radiation, concentrating on the inverse square potential and the exponential potential for the tachyonic scalar field. A distinguishing feature of these models (compared to other cosmological models) is that the matter density parameter and the density parameter for tachyons remain comparable even in the matter dominated phase. For the exponential potential, the solutions have an accelerating phase, followed by a phase with a(t) ∝ t 2/3 as t → ∞. This eliminates the future event horizon present in ΛCDM models and is an attractive feature from the string theory perspective. A comparison with supernova Ia data shows that for both the potentials there exists a range of models in which the universe undergoes an accelerated expansion at low redshifts and are also consistent with requirements of structure formation. They do require fine tuning of parameters but not any more than in the case of ΛCDM or quintessence models. I. MOTIVATIONObservations suggest that our universe has entered a phase of accelerated expansion in the recent past. Friedmann equations can be consistent with such an accelerated expansion only if the universe is populated by a medium with negative pressure. One of the possible sources which could provide such a negative pressure will be a scalar field with either of the following two types of Lagrangians:Both these Lagrangians involve one arbitrary function V (φ). The first one L quin , which is a natural generalization of the Lagrangian for a nonrelativistic particle, L = (1/2)q 2 − V (q), is usually called quintessence (for a sample of models, see Ref.[1]). When it acts as a source in Friedmann universe, it is characterized by a time dependent w(t) ≡ (P/ρ) withJust as L quin generalizes the Lagrangian for the nonrelativistic particle, L tach generalizes the Lagrangian for the relativistic particle [2]. A relativistic particle with a (one dimensional) position q(t) and mass m is described by the Lagrangian L = −m 1 −q 2 . It has the energy E = m/ 1 −q 2 and momentum p = mq/ 1 −q 2 which are related by E 2 = p 2 +m 2 . As is well known, this allows the possibility of having massless particles with finite energy for which E 2 = p 2 . This is achieved by taking the limit of m → 0 andq → 1, while keeping the ratio in E = m/ 1 −q 2 finite. The momentum acquires a life of its own, unconnected with the velocityq, and the energy is expressed in terms of the momentum (rather than in terms ofq) in the Hamiltonian formulation. We can now construct a field theory by upgrading q(t) to a field φ. Relativistic invariance now requires φ to depend on both space and time [φ = φ(t, x)] andq 2 to be replaced by ∂ i φ∂ i φ. It is also possible now to treat the mass parameter m as a function of φ, say, V (φ) thereby obtaining a field theoretic Lagrangian L = −V (φ) 1 − ∂ i φ∂ i φ. The Hamiltonian structure of this theory is algebraically very similar to the special relativistic example we starte...

The conceptual difficulties associated with a cosmological constant have led to the investigation of alternative models in which the equation of state parameter, $w=p/\rho$, of the dark energy evolves with time. We show that combining the supernova type Ia observations {\it with the constraints from WMAP observations} restricts large variation of $\rho(z)$ at low redshifts. The combination of these two observational constraints is stronger than either one. The results are completely consistent with the cosmological constant as the source of dark energy.Comment: Final version to appear in MNRAS (Letters); discussion enlarged and clarifications and references added; 6 pages; 3 figure

A gamma‐ray burst (GRB) releases an amount of energy similar to that of a supernova explosion, which combined with its rapid variability suggests an origin related to neutron stars or black holes. Since these compact stellar remnants form from the most massive stars not long after their birth, GRBs should trace the star formation rate in the Universe; we show that the GRB flux distribution is consistent with this. Because of the strong evolution of the star formation rate with redshift, it follows that the dimmest known bursts have z ∼ 6, much above the value usually quoted and beyond the most distant quasars. This explains the absence of bright galaxies in well‐studied GRB error boxes. The increased distances imply a peak luminosity of 8.3 × 1051 erg s−1 and a rate density of 0.025 per million years per galaxy. These values are 20 times higher and 150 times lower, respectively, than are implied by fits with non‐evolving GRB rates. This means either that GRBs are caused by a much rarer phenomenon than mergers of binary neutron stars, or that their gamma‐ray emission is often invisible to us due to beaming. Precise burst locations from optical transients will discriminate between the various models for GRBs from stellar deaths, because the distance between progenitor birth place and burst varies greatly among them. The dimmest GRBs are then the most distant known objects, and may probe the Universe at an age when the first stars were forming.

We model the distribution of neutral hydrogen (H i) in the post‐reionization universe. This model uses gravity‐only N‐body simulations and an ansatz to assign H i to dark matter haloes that is consistent with observational constraints and theoretical models. We resolve the smallest haloes that are likely to host H i in the simulations; care is also taken to ensure that any errors due to the finite size of the simulation box are small. We then compute the smoothed one‐point probability distribution function and the power spectrum of fluctuations in H i. This is compared with other predictions that have been made using different techniques. We highlight the significantly high bias for the H i distribution at small scales. This aspect has not been discussed before. We then discuss the prospects of the detection with the Murchison Widefield Array (MWA), Giant Meterwave Radio Telescope (GMRT) and the hypothetical MWA5000. The MWA5000 can detect visibility correlations at large angular scales at all redshifts in the post‐reionization era. The GMRT can detect visibility correlations at lower redshifts; specifically there is a strong case for a survey at z≃ 1.3. We also discuss prospects for direct detection of rare peaks in the H i distribution using the GMRT. We show that direct detection should be possible with an integration time that is comparable to, or even less than, the time required for a statistical detection. Specifically, it is possible to make a statistical detection of the H i distribution by measuring the visibility correlation and direct detection of rare peaks in the H i distribution at z≃ 1.3 with the GMRT in less than 1000 h of observations.