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It is possible that fundamental constants may not be constant at all. There is a generally accepted view that one can only talk about variations of dimensionless quantities, such as the fine structure constant $\alpha_{\rm e}\equiv e^2/4\pi\epsilon_0\hbar c$. However, constraints on the strength of gravity tend to focus on G itself, which is problematic. We stress that G needs to be multiplied by the square of a mass, and hence, for example, one should be constraining $\alpha_{\rm g}\equiv G m_{\rm p}^2/\hbar c$, where $m_{\rm p}$ is the proton mass. Failure to focus on such dimensionless quantities makes it difficult to interpret the physical dependence of constraints on the variation of G in many published studies. A thought experiment involving talking to observers in another universe about the values of physical constants may be useful for distinguishing what is genuinely measurable from what is merely part of our particular system of units., Comment: 6 pages, Gravity Research Foundation essay

We use present cosmological data from the cosmic microwave background, large-scale structure and deuterium at high redshifts to constrain supersymmetric F- and D-term hybrid inflation scenarios including possible contributions to the CMB anisotropies from cosmic strings. Using two different realizations of the cosmic string spectrum, we find that the minimal version of the D-term model is ruled out at high significance. F-term models are also in tension with the data. We also discuss possible non-minimal variants of the models., Comment: 4 pages, 2 figures

If the equation of state of dark energy is anisotropic there will be additional quadrupole anisotropy in the cosmic microwave background induced by the time dependent anisotropic stress quantified in terms of $\Delta w$. Assuming that the entire amplitude of the observed quadrupole is due to this anisotropy, we conservatively impose a limit of $|\Delta w| < 2.1\times 10^{-4}$ for any value of $w\ge -1$ assuming that $\Omega_{\rm m}<0.5$. This is considerably tighter than that which comes from SNe. Stronger limits, upto a factor of 10, are possible for specific values of $\Omega_{\rm m}$ and $w$. Since we assume this component is uncorrelated with the stochastic component from inflation, we find that both the expectation value and the sample variance are increased. There no improvement in the likelihood of an anomalously low quadrupole as suggested by previous work on an elliptical universe.

We investigate the breaking of global statistical isotropy caused by a dark energy component with an energy-momentum tensor which has point symmetry, that could represent a cubic or hexagonal crystalline lattice. In such models Gaussian, adiabatic initial conditions created during inflation can lead to anisotropies in the cosmic microwave background whose spherical harmonic coefficients are correlated, contrary to the standard assumption. We develop an adaptation of the line of sight integration method that can be applied to models where the background energy-momentum tensor is isotropic, but whose linearized perturbations are anisotropic. We then show how this can be applied to the cases of cubic and hexagonal symmetry. We compute quantities which show that such models are indistinguishable from isotropic models even in the most extreme parameter choices, in stark contrast to models with anisotropic initial conditions based on inflation. The reason for this is that the dark energy based models contribute to the CMB anistropy via the inegrated Sachs-Wolfe effect, which is only relevent when the dark energy is dominant, that is, on the very largest scales. For inflationary models, however, the anisotropy is present on all scales., Comment: 18 pages, 9 figures

Structure in the Universe grew through gravitational instability from very smooth initial conditions. Energy conservation requires that the growing negative potential energy of these structures is balanced by an increase in kinetic energy. A fraction of this is converted into heat in the collisional gas of the intergalactic medium. Using a toy model of gravitational heating we attempt to link the growth of structure in the Universe and the average temperature of this gas. We find that the gas is rapidly heated from collapsing structures at around $z {\sim} 10$, reaching a temperature ${>} 10^6$K today, depending on some assumptions of our simplified model. Before that there was a cold era from $z\sim100$ to $\sim10$ in which the matter temperature is below that of the Cosmic Microwave Background., Comment: 6 pages, 3 figures, Gravity Research Foundation essay

The temperature of the atomic matter in the Universe is held to that of the Cosmic Background radiation until decoupling at z~100. After this it cools faster than the radiation (\propto(1+z)^2 rather than (1+z)) and would have fallen to about 20mK today if astrophysical feedback processes had not heated up the interglactic medium. We show how the derivative of the Compton coupling equation helps numerically to follow the decoupling process., Comment: 2 pages, short and sweet, MNRAS in press, revised to match accepted version

Acoustic modes can be used to study the physics of the interior of a cavity, and this is especially useful when the inside region is inaccessible. Many astrophysicists use such sound waves as an essential tool in their research. Here we focus on two separate sub-fields in which oscillations on the surface of a sphere are studied -- Helioseismology and CMBology -- the surface being either the solar or cosmic photosphere. Both research areas use the language of spherical harmonics, as well as sharing many close similarities in the underlying physics. However, there are also many fundamental differences, which we explain in this pedagogical article., Comment: 10 pages, 4 figures

The major theoretical limitation for extracting cosmological parameters from the CMB sky lies in the precision with which we can calculate the cosmological recombination process. Uncertainty in the details of hydrogen and helium recombination could effectively increase the errors or bias the values of the cosmological parameters derived from the Planck satellite, for example. Here we modify the cosmological recombination code RECFAST by introducing one more parameter to reproduce the recent numerical results for the speed-up of the helium recombination. Together with the existing hydrogen fudge factor, we vary these two parameters to account for the remaining dominant uncertainties in cosmological recombination. By using the CosmoMC code with Planck forecast data, we find that we need to determine the parameters to better than ten per cent for He I and one per cent for H, in order to obtain negligible effects on the cosmological parameters. For helium recombination, if the existing studies have calculated the ionization fraction to the 0.1 per cent level by properly including the relevant physical processes, then we already have numerical calculations which are accurate enough for Planck. For hydrogen, setting the fudge factor to speed up low redshift recombination by 14 per cent appears to be sufficient for Planck. However, more work still needs to be done to carry out comprehensive numerical calculations of all the relevant effects for hydrogen, as well as to check for effects which couple hydrogen and helium recombinaton through the radiation field., Comment: 6 pages, 6 figures; Paper revised according to the reviewer's suggestions. An updated RECFAST (version 1.4) available at http://www.astro.ubc.ca/people/scott/recfast.html

By considering simple, but representative, models of brane inflation from a single brane-antibrane pair in the slow roll regime, we provide constraints on the parameters of the theory imposed by measurements of the CMB anisotropies by WMAP including a cosmic string component. We find that inclusion of the string component is critical in constraining parameters. In the most general model studied, which includes an inflaton mass term, as well as the brane-antibrane attraction, values n_s < 1.02 are compatible with the data at 95 % confidence level. We are also able to constrain the volume of internal manifold (modulo factors dependent on the warp factor) and the value of the inflaton field to be less than 0.66M_P at horizon exit. We also investigate models with a mass term. These observational considerations suggest that such models have r < 2*10^-5, which can only be circumvented in the fast roll regime, or by increasing the number of antibranes. Such a value of r would not be detectable in CMB polarization experiment likely in the near future, but the B-mode signal from the cosmic strings could be detectable. We present forecasts of what a similar analysis using PLANCK data would yield and find that it should be possible to rule out G\mu > 6.5*10^-8 using just the TT, TE and EE power spectra., Comment: 11 pages, 3 figures, revtex4, typos corrected, references added

Most cosmological parameters are expected to change significantly only on cosmological time scales, but given the large amount of information contained within the Cosmic Microwave Background (CMB) sky, we can expect that changes in the CMB should be observable on much shorter time scales. Here we quantify this expectation, examining the detectability of the dominant effects on short time scales. We find that an ideal future experiment with currently achievable sensitivity could detect the changing dipole due to our galactic motion in about 10 years, but that it would take around 4000 years to detect a change in the higher order multipoles., Comment: 4 pages, 3 figures

We discuss the possibility of performing a substantial spectroscopic galaxy redshift survey selected via the 21cm emission from neutral hydrogen using the Five-hundred metre Aperture Spherical Telescope (FAST) to be built in China. We consider issues related to the estimation of the source counts and optimizations of the survey, and discuss the constraints on cosmological models that such a survey could provide. We find that a survey taking around two years could detect ~10^7 galaxies with an average redshift of ~0.15 making the survey complementary to those already carried out at optical wavelengths. These conservative estimates have used the z=0 HI mass function and have ignored the possibility of evolution. The results could be used to constrain Gamma = (Omega_m h) to 5 per cent and the spectral index, n_s, to 7 per cent independent of cosmic microwave background data. If we also use simulated power spectra from the Planck satellite, we can constrain w to be within 5 per cent of -1., Comment: 13 pages, 15 figures, Accepted by MNRAS, minor corrections

We discuss the general framework for a perfect continuum medium in cosmology and show that an interesting generalization of the fluids normally used is for the medium to have rigidity and, hence, be analogous to an elastic solid. Such models can provide perfect, adiabatic fluids which are stable even when the pressure is negative, if the rigidity is sufficiently large, making them natural candidates to describe the dark energy. In fact, if the medium is adiabatic and isotropic, they provide the most general description of linearized perturbations. We derive the equations of motion and wave propagation speeds in the isotropic case. We point out that anisotropic models can also be incorporated within the same formalism and that they are classified by the standard Bravais Lattices. We identify the adiabatic and isocurvature modes allowed in both the scalar and vector sectors and discuss the predictions they make for CMB and matter power spectra. We comment on the relationship between these models and other fluid-based approaches to dark energy, and discuss a possible microphysical manifestation of this class of models as a continuum description of defect-dominated scenarios., Comment: 29 pages, 12 figures

We point out that the inclusion of a string component contributing around 5% to the CMB power spectrum amplitude on large scales can increase the preferred value of the spectral index n_s of density fluctuations measured by CMB experiments. While this finding applies to any cosmological scenario involving strings, we consider in particular models of supersymmetric hybrid inflation, which predict n_s >= 0.98, in tension with the CMB data when strings are not included. Using MCMC analysis we constrain the parameter space allowed for F- and D-term inflation. For the F-term model, using minimal supergravity corrections, we find that \log\kappa= -2.34\pm 0.38 and M= (0.518\pm 0.059) * 10^16 GeV. The inclusion of non-minimal supergravity corrections can modify these values somewhat. In the corresponding analysis for D-term inflation, we find \log\kappa= -4.24\pm 0.19 and m_FI= (0.245\pm 0.031) * 10^16 GeV. Under the assumption that these models are correct, these results represent precision measurements of important parameters of a Grand Unified Theory. We consider the possible uncertainties in our measurements and additional constraints on the scenario from the stochastic background of gravitational waves produced by the strings. The best-fitting model predicts a B-mode polarization signal \approx 0.3 \mu K rms peaking at l \approx 1000. This is of comparable amplitude to the expected signal due to gravitational lensing of the adiabatic E-mode signal on these scales., Comment: 21 pages, 16 figures

A variety of observational tests seem to suggest that the universe is anisotropic. This is incompatible with the standard dogma based on adiabatic, rotationally invariant perturbations. We point out that this is a consequence of the standard decomposition of the stress-energy tensor for the cosmological fluids, and that rotational invariance need not be assumed, if there is elastic rigidity in the dark energy. The dark energy required to achieve this might be provided by point symmetric domain wall network with $P/\rho=-2/3$, although the concept is more general. We illustrate this with reference to a model with cubic symmetry and discuss various aspects of the model., Comment: 4 pages, 3 figures

Interest in the elastic properties of regular lattices constructed from domain walls has recently been motivated by cosmological applications as solid dark energy. This work investigates the particularly simple examples of triangular, hexagonal and square lattices in two dimensions and a variety of more complicated lattices in three dimensions which have cubic symmetry. The relevant rigidity coefficients are computed taking into account non-affine perturbations where necessary, and these are used to evaluate the propagation velocity for any macroscopic scale perturbation mode. Using this information we assess the stability of the various configurations., Comment: 16 pages, 7 figures

If the dark energy is modelled as a relativistic elastic solid then the standard CDM and $\Lambda$CDM models, as well as lattice configurations of cosmic strings or domain walls, are points in the two-dimensional parameter space $(w,c_{\rm s}^2)$. We present a detailed analysis of the best fitting cosmological parameters in this model using data from a range of observations. We find that the $\chi^2$ is improved by $\sim 10$ by including the two parameters and that the $w=-1$ $\Lambda$CDM model is only the best fit to the data when a large number of different datasets are included. Using CMB observations alone we find that $w=-0.38\pm 0.16 $ and with the addition of Large-Scale Structure data $w=-0.62\pm 0.15 $ and $\log c_{\rm s}=-0.77\pm 0.28$. We conclude that the models based on topological defects provide a good fit to the current data, although $\Lambda$CDM cannot be ruled out., Comment: 10 pages