Simultaneous calculation of the dipole moment μ_j and the relaxation time τ_j of a certain number of non-spherical rigid aliphatic polar liquid molecules (j) in non-polar solvents (i) under 9.8 GHz electric field is possible from real ε′_ij and imaginary ε″_ij parts of the complex relative permittivity ε*_ij. The low frequency and infinite frequency permittivities ε_0ij and ε_∞ij measured by Purohitet al [1,2] and Srivastava and Srivastava [3] at 25, 35 and 30°C respectively are used to obtain static μ_s. The ratio of the individual slopes of imaginary σ″_ij and real σ′_ij parts of high frequency (hf) complex conductivity σ*_ij with weight fractionsw_jatw_j → 0 and the slopes of σ″_ij— σ′_ij curves for differentw_js [4] are employed to obtain τ_js. The former method is better in comparison to the existing one as it eliminates polar-polar interaction. The hf μ_js in Coulomb metre (C m) when compared with static and reported μs indicate that μ_s s favour the monomer formations which combine to form dimers in the hf electric field. The comparison among μs shows that a part of the molecule is rotating under X-band electric field [5]. The theoretical μ_theos from available bond angles and bond moments of the substituent polar groups attached to the parent molecules differ from the measured μ_js and μs to establish the possible existence of mesomeric, inductive and electromeric effects in polar liquid molecules.

The dielectric relaxation times $\tau_{jk}$'s and dipole moments $\mu_{jk}$'s of the binary ($j_{k}$) polar liquid mixture of N,N-dimethyl acetamide (DMA) and acetone (Ac) dissolved in benzene (i) are estimated from the measured real $\sigma_{ijk}^{'}$ and imaginary $\sigma_{ijk}^{''}$ parts of complex high frequency conductivity $\sigma_{ijk}^{*}$ of the solution for different weight fractions $w_{jk}$'s of 0.0, 0.3, 0.5, 0.7 and 1.0 mole fractions $x_{j}$ of Ac and temperatures (25, 30, 35 and 40°C) respectively under 9.88 GHz electric field. $\tau_{jk}$'s are obtained from the ratio of slopes of $\sigma_{ijk}^{''} - w_{jk}$ and $\sigma_{ijk}^{'} - w_{jk}$ curves at $w_{jk} \rightarrow 0$ as well as linear slope of $\sigma_{ijk}^{''} - \sigma_{ijk}^{'}$ curves of the existing method (Murthy et al, 1989) in order to eliminate polar-polar interaction in the latter case. The calculated 𝜏's are in excellent agreement with the reported 𝜏's due to Gopalakrishna's method. $\mu_{jk}$'s are also estimated from slopes 𝛽's of total conductivity $\sigma_{ijk} - w_{jk}$ curves at $w_{jk} \rightarrow 0$ and the values agree well with the reported 𝜇's from G.K. method. The variation of $\tau_{jk}$'s and $\mu_{jk}$'s with $x_{j}$ of Ac reveals that solute-solute molecular association occurs within $0.0-0.3x_{j}$ of Ac beyond which solute-solvent molecular association is predicted. The theoretical dipole moments $\mu_{\text{theo}}$'s are calculated from bond angles and bond moments to have exact 𝜇's only to show the presence of inductive, mesomeric and electromeric effects in the substituent polar groups. The thermodynamic energy parameters are estimated from ln($\tau_{jk}T$) against $1/T$ linear curve from Eyring's rate theory to know the molecular dynamics of the system and to establish the fact that the mixture obeys the Debye-Smyth relaxation mechanism.

This is the report of the cosmology and astroparticle physics working group at WHEPPXI. We present the discussions carried out during the workshop on selected topics in the above fields. The problems discussed concerned axions, infrared divergences in inflationary theories, supersonic bubbles in a first-order electroweak phase transition, dark matter, MOND, interacting dark energy, composite Higgs models and statistical anisotropy of the Universe.