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

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

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

Integrating 3D Printing Technologies into Architectural Education as Design Tools

3D printing technology offers the chance to produce very small-scale, complex forms that could help to improve educational materials for architectural design. In this age of technological advances, architectural education needs to integrate modern teaching methods that could enhance students’ visual perception. This research thus examined the impact of computational design modeling and 3D printing technology on the spatial cognition of architecture students. It starts with the premise that the use of the 3D printed models will support design logic and improve the deep understanding of spatial perception among students. Thirty architecture students were asked about a designed project realized for the purpose of this study. They were presented both a project designed via computer modeling software and a printed model of the same project. The outcomes indicate that the use of 3D printing gave better results in the development of students’ spatial abilities. The findings also confirm that adopting this technology in the development of teaching tools will enhance students’ spatial perception and extend beyond the seamless materialization of the digital model which can continuously inform design ideation through emerging perception qualities