Finite measure for the initial conditions of inflation

We investigate whether inflation requires finely tuned initial conditions in order to explain the degree of flatness and homogeneity observed in the Universe. We achieve this by using the Eisenhart lift, which can be used to write any scalar field theory in a purely geometric manner. Using this formalism, we construct a manifold whose points represent all possible initial conditions for an inflationary theory. After equipping this manifold with a natural metric, we show that the total volume of this manifold is finite for a wide class of inflationary potentials. Hence, we identify a natural measure that enables us to distinguish between generic and finely tuned sets of initial conditions without the need for a regulator, in contrast to previous work in the literature. Using this measure, we find that the initial conditions that allow for sufficient inflation are indeed finely tuned. The degree of fine-tuning also depends crucially on the value of the cosmological constant at the time of inflation. Examining some concrete examples, we find that we require percent-level fine tuning if we allow the cosmological constant during inflation to be much larger than it is today. However, if we fix the cosmological constant to its presently observed value, the degree of fine tuning required is of order $10^{-54}$

Cardiovascular magnetic resonance by non contrast T1-mapping allows assessment of severity of injury in acute myocardial infarction

BACKGROUND: Current cardiovascular magnetic resonance (CMR) methods, such as late gadolinium enhancement (LGE) and oedema imaging (T2W) used to depict myocardial ischemia, have limitations. Novel quantitative T1-mapping techniques have the potential to further characterize the components of ischemic injury. In patients with myocardial infarction (MI) we sought to investigate whether state-of the art pre-contrast T1-mapping (1) detects acute myocardial injury, (2) allows for quantification of the severity of damage when compared to standard techniques such as LGE and T2W, and (3) has the ability to predict long term functional recovery. METHODS: 3T CMR including T2W, T1-mapping and LGE was performed in 41 patients [of these, 78% were ST elevation MI (STEMI)] with acute MI at 12-48 hour after chest pain onset and at 6 months (6M). Patients with STEMI underwent primary PCI prior to CMR. Assessment of acute regional wall motion abnormalities, acute segmental damaged fraction by T2W and LGE and mean segmental T1 values was performed on matching short axis slices. LGE and improvement in regional wall motion at 6M were also obtained. RESULTS: We found that the variability of T1 measurements was significantly lower compared to T2W and that, while the diagnostic performance of acute T1-mapping for detecting myocardial injury was at least as good as that of T2W-CMR in STEMI patients, it was superior to T2W imaging in NSTEMI. There was a significant relationship between the segmental damaged fraction assessed by either by LGE or T2W, and mean segmental T1 values (P < 0.01). The index of salvaged myocardium derived by acute T1-mapping and 6M LGE was not different to the one derived from T2W (P = 0.88). Furthermore, the likelihood of improvement of segmental function at 6M decreased progressively as acute T1 values increased (P < 0.0004). CONCLUSIONS: In acute MI, pre-contrast T1-mapping allows assessment of the extent of myocardial damage. T1-mapping might become an important complementary technique to LGE and T2W for identification of reversible myocardial injury and prediction of functional recovery in acute MI