Are there really conformal frames? Uniqueness of affine inflation

Here we concisely review the nonminimal coupling dynamics of a single scalar field in the context of purely affine gravity and extend the study to multifield dynamics. The coupling is performed via an affine connection and its associated curvature without referring to any metric tensor. The latter arises a posteriori and it may gain an emergent character like the scale of gravity. What is remarkable in affine gravity is the transition from nonminimal to minimal couplings which is realized by only field redefinition of the scalar fields. Consequently, the inflationary models gain a unique description in this context where the observed parameters, like the scalar tilt and the tensor-to-scalar ratio, are invariant under field reparametrization. Overall, gravity in its affine approach is expected to reveal interesting and rich phenomenology in cosmology and astroparticle physics.Comment: Review Article: matches the published version in IJMPD, 44 pages, 1 table and 2 figure

Eddington's Gravity in Immersed Spacetime

We formulate Eddington's affine gravity in a spacetime which is immersed in a larger eight dimensional space endowed with a hypercomplex structure. The dynamical equation of the first immersed Ricci-type tensor leads to gravitational field equations which include matter. We also study the dynamical effects of the second Ricci-type tensor when added to the Lagrangian density. A simple Lagrangian density constructed from combination of the standard Ricci tensor and a new tensor field that appears due to the immersion, leads to gravitational equations in which the vacuum energy gravitates with a different cosmological strength as in Phys. Rev. D {\bf 90}, 064017 (2014), rather than with Newton's constant. As a result, the tiny observed curvature is reproduced due to large hierarchies rather than fine-tuning

Removal of endocrine disrupting chemicals using low pressure reverse osmosis membrane

Endocrine disrupting chemicals (EDCs) are one of the major focuses of contaminants in current environmental issues, as they can cause adverse health effects on animals and human, particularly to endocrine function. The objective of this study was to remove a specific group of EDCs (i.e molecular weight range 228 to 288 g/mol) using low pressure reverse osmosis membrane (LPROM). A multi-layer thin-film composite of aromatic polyamide (ES20) membrane and a C10-T cross flow module of LPROM manufactured by Nitto Denko Company was used in this study. The effects of operating parameters, i.e. pH, operating pressure, concentration and temperature were observed using a design of experiment based on MINITABTM software. The analysis of results was conducted by factorial analysis (FA) and response surface analysis (RSA). It was found that LPROM has been effectively applied to remove pentachlorophenol (PCP) (more than 83%), 17ß-estradiol (more than 87%) and bisphenol-A (BPA) (more than 87%). For permeate flux, both PCP and 17ß-estradiol tests produce excellent flux rate; i.e. 23.8 L/m2.h and 22.9 L/m2.h, respectively. For BPA, the permeate flux produced was slightly lower (19.1 L/m2.h) due to its physical-chemical properties effect at various levels of the recovery rate. In this study, the percentage of rejection was increased with the increased of pH and concentration of compounds. The flux was observed to increase with the increase of operating pressure. This study also investigated the interaction effects between operating parameters involved. In addition, statistical models were developed to represent the performance of LPROM under two response parameters, i.e. percentage of EDCs rejection and permeate flux. Statistical models were then validated using One-Factor-At-a-Time (OFAT) design of experiments and comparisons were made to better understand the trend of EDCs rejection and permeate flux

Separate Einstein-Eddington Spaces and the Cosmological Constant

Based on Eddington affine variational principle on a locally product manifold, we derive the separate Einstein space described by its Ricci tensor. The derived field equations split into two field equations of motion that describe two maximally symmetric spaces with two cosmological constants. We argue that the invariance of the bi-field equations under projections on the separate spaces, may render one of the cosmological constants to zero. We also formulate the model in the presence of a scalar field. The resulted separate Einstein-Eddington spaces maybe considered as two states that describe the universe before and after inflation. A possibly interesting affine action for a general perfect fluid is also proposed. It turns out that the condition which leads to zero cosmological constant in the vacuum case, eliminates here the effects of the gravitational mass density of the perfect fluid, and the dynamic of the universe in its final state is governed by only the inertial mass density of the fluid.Comment: Accepted in Annalen der Physik journal. 7 pages, typos correcte

Affine Inflation

Affine gravity, a gravity theory based on affine connection with no notion of metric, supports scalar field dynamics only if scalar fields have non-vanishing potential. The non-vanishing vacuum energy ensures that the cosmological constant is non-vanishing. It also ensures that the energy-momentum tensor of vacuum gives the dynamically generated metric tensor. We construct this affine setup and study primordial inflation in it. We study inflationary dynamics in affine gravity and general relativity, comparatively. We show that non-minimally coupled inflaton dynamics can be transformed into a minimally-coupled one with a modified potential. We also show that there is one unique frame in affine gravity, as opposed to the Einstein and Jordan frames in general relativity. Future observations with higher accuracy may be able to test the affine gravity.Comment: 10 pages, 3 figures, 3 tables. With the correct journal referenc

Induced Affine Inflation

Induced gravity, metrical gravity in which gravitational constant arises from vacuum expectation value of a heavy scalar, is known to suffer from Jordan frame vs. Einstein frame ambiguity, especially in inflationary dynamics. Induced gravity in affine geometry, as we show here, leads to an emergent metric and gravity scale, with no Einstein-Jordan ambiguity. While gravity is induced by the vacuum expectation value of the scalar field, nonzero vacuum energy facilitates generation of the metric. Our analysis shows that induced gravity results in a relatively large tensor-to-scalar ratio in both metrical and affine gravity setups. However, the fact remains that the induced affine gravity provides an ambiguity-free framework.Comment: 7 pages, 1 table and 3 figures, matches the published versio